| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
y^{\prime }&=2 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.572 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
2.493 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.111 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.489 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.734 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.347 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.142 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime }&=\left (y+1\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.763 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.185 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| \begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.664 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x} \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.977 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.512 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.059 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.896 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.928 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.409 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.530 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.931 |
|
| \begin{align*}
x y^{\prime }+5 y&=7 x^{2} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.884 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
3 x y^{\prime }+y&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
x y^{\prime }-y&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.415 |
|
| \begin{align*}
2 x y^{\prime }-3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.561 |
|
| \begin{align*}
x y^{\prime }+3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.034 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| \begin{align*}
x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.812 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \begin{align*}
x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.684 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| \begin{align*}
x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
\frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.469 |
|
| \begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.104 |
|
| \begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.769 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
x y^{\prime }&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.642 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.465 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.817 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.563 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.684 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.714 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.782 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.489 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.697 |
|
| \begin{align*}
x y y^{\prime }&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.947 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.546 |
|
| \begin{align*}
y y^{\prime }+x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.661 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.601 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.414 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| \begin{align*}
2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.745 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| \begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.343 |
|
| \begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.667 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.700 |
|
| \begin{align*}
y^{\prime }&=f \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
x y^{\prime }-4 x^{2} y+2 \ln \left (y\right ) y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.036 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.345 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.608 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
y^{\prime }+2 y x&=1+x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.022 |
|
| \begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.248 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.076 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.569 |
|
| \begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| \begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.524 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.110 |
|
| \begin{align*}
4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.195 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.204 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.809 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.162 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| \begin{align*}
x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.431 |
|
| \begin{align*}
9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.539 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.554 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.265 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.550 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{y-3 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.902 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.600 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.770 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
y^{\prime }&=2 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.023 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
9.203 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (y+1\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.369 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.323 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| \begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.792 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x} \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.437 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.726 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.181 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.388 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.304 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.657 |
|
| \begin{align*}
3 x y^{\prime }+y&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
x y^{\prime }-y&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.860 |
|
| \begin{align*}
2 x y^{\prime }-3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
x y^{\prime }+3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.762 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \begin{align*}
x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.976 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.108 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.250 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.484 |
|
| \begin{align*}
x y^{\prime }&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.330 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.213 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.997 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.692 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.803 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.065 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.133 |
|
| \begin{align*}
x y y^{\prime }&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.594 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.413 |
|
| \begin{align*}
y y^{\prime }+x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.233 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.720 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.131 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
x y^{\prime }+6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.372 |
|
| \begin{align*}
2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.172 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.941 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| \begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.412 |
|
| \begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.993 |
|
| \begin{align*}
3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.119 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.339 |
|
| \begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.112 |
|
| \begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.881 |
|
| \begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.314 |
|
| \begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.093 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.697 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.396 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.887 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.032 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.959 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.826 |
|
| \begin{align*}
x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.835 |
|
| \begin{align*}
9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.177 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.435 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.433 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.336 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{y-3 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.753 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.605 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.078 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
2 y t +y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.812 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
-y+t y^{\prime }&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.088 |
|
| \begin{align*}
2 y+t y^{\prime }&=t^{2}-t +1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.773 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
-y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
\frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \begin{align*}
-\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.070 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.921 |
|
| \begin{align*}
y^{\prime }&=\left (1-2 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{6}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.348 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.519 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| \begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.300 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.194 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.795 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.329 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.436 |
|
| \begin{align*}
x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.106 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.401 |
|
| \begin{align*}
y+\left (-4+t \right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.415 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.247 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| \begin{align*}
y^{\prime }&=y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.312 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.824 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
18.016 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x -b y}{b x +c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.465 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x +b y}{b x -c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.022 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.673 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.365 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| \begin{align*}
y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| \begin{align*}
3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.818 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}-2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| \begin{align*}
y^{\prime }&=3-6 x +y-2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
y x +x y^{\prime }&=1-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.701 |
|
| \begin{align*}
x +y+\left (x +2 y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.725 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }&=y-y \,{\mathrm e}^{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.056 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+3 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.029 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.537 |
|
| \begin{align*}
3 t +2 y&=-t y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.321 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.434 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.555 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
30.531 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
2 y^{\prime }+x \left (y^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\
y \left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| \begin{align*}
y^{\prime }&=x \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.647 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y+1\right )}{x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.891 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.453 |
|
| \begin{align*}
x y^{\prime }+3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.420 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \begin{align*}
x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.272 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
y^{\prime }+\frac {k y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| \begin{align*}
y^{\prime }+\tan \left (k x \right ) y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \begin{align*}
y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.926 |
|
| \begin{align*}
x y^{\prime }+\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.067 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| \begin{align*}
\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
x y^{\prime }+2 y&=8 x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.669 |
|
| \begin{align*}
x y^{\prime }-2 y&=-x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.583 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x y^{\prime }-2 y&=-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.168 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.384 |
|
| \begin{align*}
\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )}&=-\frac {3}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.819 |
|
| \begin{align*}
x y^{\prime }+y^{2}+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.396 |
|
| \begin{align*}
x^{2} y y^{\prime }&=\left (y^{2}-1\right )^{{3}/{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.206 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| \begin{align*}
y^{\prime }&=\left (x -1\right ) \left (-1+y\right ) \left (-2+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.507 |
|
| \begin{align*}
\left (-1+y\right )^{2} y^{\prime }&=2 x +3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }+x \left (y^{2}+y\right )&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
y^{\prime }+2 x \left (y+1\right )&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \begin{align*}
y^{\prime }&=2 x y \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.596 |
|
| \begin{align*}
y^{\prime } \left (x^{2}+2\right )&=4 x \left (y^{2}+2 y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| \begin{align*}
y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.504 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.404 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.565 |
|
| \begin{align*}
y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.773 |
|
| \begin{align*}
\left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.433 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.372 |
|
| \begin{align*}
x y^{\prime }-2 y&=\frac {x^{6}}{x^{2}+y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.619 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.569 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.158 |
|
| \begin{align*}
y^{\prime }&=\frac {\tan \left (y\right )}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.016 |
|
| \begin{align*}
y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\
y \left (0\right ) &= 9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
42.148 |
|
| \begin{align*}
y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\
y \left (3\right ) &= -7 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
11.588 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.688 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.746 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.716 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.181 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}+x^{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
98.177 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.595 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.100 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.547 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.059 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.503 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.773 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-3 y x -5 x^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.773 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 x^{2}+y^{2}+4 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.141 |
|
| \begin{align*}
x y y^{\prime }&=3 x^{2}+4 y^{2} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.819 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.168 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (\ln \left (y\right )-\ln \left (x \right )\right )&=x \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.729 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.307 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.868 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.434 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.865 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -4 x^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.665 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.821 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
46.084 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.360 |
|
| \begin{align*}
y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.878 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.877 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.691 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=y^{3}+x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
x y y^{\prime }&=3 x^{6}+6 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.185 |
|
| \begin{align*}
x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.246 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| \begin{align*}
2 x \left (y+2 \sqrt {x}\right ) y^{\prime }&=\left (y+\sqrt {x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.895 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 x^{2} y^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.243 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=\frac {3 y^{2} x^{4}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.579 |
|
| \begin{align*}
y^{\prime }&=1+x -\left (2 x +1\right ) y+x y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.451 |
|
| \begin{align*}
2 x +y+\left (2 y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.383 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.759 |
|
| \begin{align*}
{\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.749 |
|
| \begin{align*}
\left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.692 |
|
| \begin{align*}
7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.893 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.531 |
|
| \begin{align*}
y^{\prime }+2 y x&=-\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
11.829 |
|
| \begin{align*}
y+\left (2 x +\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.181 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.642 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
3 x^{2} y+2 x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.676 |
|
| \begin{align*}
5 y x +2 y+5+2 x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.706 |
|
| \begin{align*}
x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.662 |
|
| \begin{align*}
-y+\left (x^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
\sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.526 |
|
| \begin{align*}
2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.440 |
|
| \begin{align*}
x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.282 |
|
| \begin{align*}
12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.888 |
|
| \begin{align*}
3 x^{2} y^{2}+2 y+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.267 |
|
| \begin{align*}
y^{\prime }+y^{2}+4 y x +4 x^{2}+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| \begin{align*}
\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.320 |
|
| \begin{align*}
\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.031 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.841 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\
y \left (0\right ) &= \sqrt {5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
y^{\prime }-2 y t&=t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.949 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.067 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.992 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.233 |
|
| \begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.468 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.540 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.012 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.100 |
|
| \begin{align*}
\left (t -\sqrt {y t}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.984 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.958 |
|
| \begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.480 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.842 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.349 |
|
| \begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.477 |
|
| \begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.467 |
|
| \begin{align*}
3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.456 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\
y \left (0\right ) &= \sqrt {5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.567 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| \begin{align*}
y^{\prime }-2 y t&=t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.345 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.459 |
|
| \begin{align*}
y^{\prime }&=1-t +y^{2}-t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.045 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.696 |
|
| \begin{align*}
\left (t -\sqrt {y t}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.451 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.175 |
|
| \begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.905 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.276 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.849 |
|
| \begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.917 |
|
| \begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.771 |
|
| \begin{align*}
3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.312 |
|
| \begin{align*}
y^{\prime }&=2 t \left (1+y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.450 |
|
| \begin{align*}
y^{\prime }&=t y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.126 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.102 |
|
| \begin{align*}
x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.939 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.543 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.181 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-1+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.547 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }-y&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y+3+\cot \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.315 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.834 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.598 |
|
| \begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.833 |
|
| \begin{align*}
y&=y x +x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.650 |
|
| \begin{align*}
y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.615 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.245 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.194 |
|
| \begin{align*}
1+y^{2}&=\frac {y^{\prime }}{x^{3} \left (x -1\right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.173 |
|
| \begin{align*}
\left (x^{2}+3 x \right ) y^{\prime }&=y^{3}+2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
17.432 |
|
| \begin{align*}
\left (x^{2}+x +1\right ) y^{\prime }&=y^{2}+2 y+5 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.212 |
|
| \begin{align*}
\left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.210 |
|
| \begin{align*}
x +y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.143 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.833 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.621 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.216 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.432 |
|
| \begin{align*}
y y^{\prime }+x&=2 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.949 |
|
| \begin{align*}
x y^{\prime }-y+\sqrt {y^{2}-x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.832 |
|
| \begin{align*}
x^{2}+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.587 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.708 |
|
| \begin{align*}
x y^{\prime }+y&=2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.920 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.026 |
|
| \begin{align*}
y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
63.104 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.714 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.066 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.293 |
|
| \begin{align*}
\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.483 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=x y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
27.343 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.881 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
y \left (6\right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.092 |
|
| \begin{align*}
\left (3 y x -2 x^{2}\right ) y^{\prime }&=2 y^{2}-y x \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
44.542 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.249 |
|
| \begin{align*}
x +y-\left (x -y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.958 |
|
| \begin{align*}
x +\left (x -2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.839 |
|
| \begin{align*}
2 x -y+1+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.507 |
|
| \begin{align*}
x -y+2+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.137 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.119 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.608 |
|
| \begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.269 |
|
| \begin{align*}
x -y+1+\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.102 |
|
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.675 |
|
| \begin{align*}
x +2 y+2&=\left (2 x +y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.651 |
|
| \begin{align*}
3 x -y+1+\left (x -3 y-5\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
59.984 |
|
| \begin{align*}
6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.547 |
|
| \begin{align*}
2 x +3 y+2+\left (-x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.699 |
|
| \begin{align*}
x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.461 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.329 |
|
| \begin{align*}
3 x -y+2+\left (x +2 y+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✓ |
✓ |
58.086 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
134.010 |
|
| \begin{align*}
x -2 y+3+\left (1-x +2 y\right ) y^{\prime }&=0 \\
y \left (-4\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.568 |
|
| \begin{align*}
2 x +y+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
y \left (-\frac {1}{6}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
16.924 |
|
| \begin{align*}
2 x +y+\left (4 x -2 y+1\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
109.997 |
|
| \begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.081 |
|
| \begin{align*}
3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.681 |
|
| \begin{align*}
a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
99.769 |
|
| \begin{align*}
2 y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
96.760 |
|
| \begin{align*}
y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \begin{align*}
\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.102 |
|
| \begin{align*}
\frac {y \left (2+x^{3} y\right )}{x^{3}}&=\frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.711 |
|
| \begin{align*}
\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}}&=\left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
20.960 |
|
| \begin{align*}
\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.514 |
|
| \begin{align*}
\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.228 |
|
| \begin{align*}
x y^{\prime }+\ln \left (x \right )-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
y x +\left (x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
64.186 |
|
| \begin{align*}
\left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.432 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.952 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.695 |
|
| \begin{align*}
\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.063 |
|
| \begin{align*}
y \left (y-x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.053 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
79.918 |
|
| \begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.313 |
|
| \begin{align*}
2 y x +\left (y-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.592 |
|
| \begin{align*}
y&=x \left (x^{2} y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.589 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+y \,{\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.833 |
|
| \begin{align*}
\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
66.040 |
|
| \begin{align*}
y \left (1-y^{2} x^{4}\right )+x y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.577 |
|
| \begin{align*}
\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.387 |
|
| \begin{align*}
x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
31.999 |
|
| \begin{align*}
\left (x^{2}+y^{2}-2 y\right ) y^{\prime }&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✗ |
✓ |
✓ |
3.863 |
|
| \begin{align*}
y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✗ |
✗ |
24.454 |
|
| \begin{align*}
x y^{\prime }+2 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.799 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.711 |
|
| \begin{align*}
y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.581 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{-y} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.053 |
|
| \begin{align*}
x y^{\prime }-2 x^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.355 |
|
| \begin{align*}
1&=\left (x +{\mathrm e}^{y}\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
x y^{\prime }&=5 y+x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \begin{align*}
2 y&=\left (y^{4}+x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.592 |
|
| \begin{align*}
y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.794 |
|
| \begin{align*}
y+2 \left (x -2 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
24.763 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.618 |
|
| \begin{align*}
x^{\prime } t +x \left (1-x^{2} t^{4}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.599 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.720 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} x^{2} \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.316 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x^{3} y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.083 |
|
| \begin{align*}
y^{\prime }&=x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.346 |
|
| \begin{align*}
2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.859 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }-y-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.150 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.951 |
|
| \begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.779 |
|
| \begin{align*}
x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.241 |
|
| \begin{align*}
2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.517 |
|
| \begin{align*}
2 y+6&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.075 |
|
| \begin{align*}
x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| \begin{align*}
-x y^{\prime }+y&=2 y^{\prime }+2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
\tan \left (y\right )&=\left (3 x +4\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.240 |
|
| \begin{align*}
y+\left (3 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.785 |
|
| \begin{align*}
r^{\prime }&=r \cot \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
\left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.800 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.563 |
|
| \begin{align*}
x +y+\left (2 x +3 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.566 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.171 |
|
| \begin{align*}
2 x y^{\prime }-y+\frac {x^{2}}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.303 |
|
| \begin{align*}
x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.205 |
|
| \begin{align*}
y \sqrt {x^{2}+y^{2}}+y x&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.096 |
|
| \begin{align*}
y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.615 |
|
| \begin{align*}
y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
63.698 |
|
| \begin{align*}
x +\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.457 |
|
| \begin{align*}
x y^{\prime }-5 y-x \sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.000 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.780 |
|
| \begin{align*}
x y^{\prime }-2 y-2 x^{4} y^{3}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.147 |
|
| \begin{align*}
x y^{\prime }&=x^{4}+4 y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} y^{6} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
x^{\prime }&=x+x^{2} {\mathrm e}^{\theta } \\
x \left (0\right ) &= 2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.503 |
|
| \begin{align*}
3 y x +\left (3 x^{2}+y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.636 |
|
| \begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| \begin{align*}
4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.709 |
|
| \begin{align*}
x -2 y+3&=\left (x -2 y+1\right ) y^{\prime } \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.043 |
|
| \begin{align*}
y^{2}+\left (x^{3}-2 y x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
✗ |
61.862 |
|
| \begin{align*}
y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
28.303 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.747 |
|
| \begin{align*}
y&=x +3 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.897 |
|
| \begin{align*}
2 y&=3 x y^{\prime }+4+2 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.124 |
|
| \begin{align*}
y&=x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| \begin{align*}
y&=x y^{\prime }+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.871 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.214 |
|
| \begin{align*}
y^{\prime }&=-x \,{\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.028 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| \begin{align*}
y^{\prime }&=\left (t^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.330 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| \begin{align*}
t y^{\prime }&=y+t^{3} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t +1} \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| \begin{align*}
t y^{\prime }&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.561 |
|
| \begin{align*}
y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\
y \left (\frac {\pi }{8}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.801 |
|
| \begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.672 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
2 x y^{\prime }+3 x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.503 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
8.500 |
|
| \begin{align*}
\left (y^{3}+x \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.137 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.445 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.693 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.353 |
|
| \begin{align*}
x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 x^{2} y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.405 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.081 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.883 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.435 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.554 |
|
| \begin{align*}
\left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.006 |
|
| \begin{align*}
x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.262 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.860 |
|
| \begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| \begin{align*}
y-\left (x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.958 |
|
| \begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.362 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.089 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.170 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.014 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.165 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.626 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.314 |
|
| \begin{align*}
\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.925 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.000 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.997 |
|
| \begin{align*}
x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.711 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.879 |
|
| \begin{align*}
2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.512 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.547 |
|
| \begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.490 |
|
| \begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.890 |
|
| \begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.484 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.840 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| \begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.372 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
y-\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.202 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.800 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.858 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.882 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.473 |
|
| \begin{align*}
x^{\prime }+\frac {2 x}{4-t}&=5 \\
x \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.770 |
|
| \begin{align*}
y-{\mathrm e}^{x}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.723 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.703 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.334 |
|
| \begin{align*}
\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.837 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.557 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.388 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| \begin{align*}
2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.908 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.263 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.455 |
|
| \begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.434 |
|
| \begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
27.258 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x +4 y}{x +y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
39.160 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.844 |
|
| \begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.933 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {4 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.632 |
|
| \begin{align*}
y^{\prime }&=\frac {x +a y}{a x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.522 |
|
| \begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.252 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.078 |
|
| \begin{align*}
2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.237 |
|
| \begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.118 |
|
| \begin{align*}
y^{\prime }&=\left (9 x -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.319 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.557 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.730 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
5.510 |
|
| \begin{align*}
y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.174 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.117 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}-y^{2}&=-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.036 |
|
| \begin{align*}
y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.572 |
|
| \begin{align*}
\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.300 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
41.040 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.175 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.212 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.860 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.695 |
|
| \begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.316 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.522 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (-1+y\right ) x +\left (-1+y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.809 |
|
| \begin{align*}
3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.316 |
|
| \begin{align*}
{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.917 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.306 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.316 |
|
| \begin{align*}
x y^{\prime }&=x +y \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.945 |
|
| \begin{align*}
{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{2 x +y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
52.214 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{-x +3 y+5} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.636 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
75.641 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.827 |
|
| \begin{align*}
y^{\prime }-y&=x^{3} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.484 |
|
| \begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.877 |
|
| \begin{align*}
x y^{\prime }-y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.636 |
|
| \begin{align*}
x y^{\prime }+n y&=x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| \begin{align*}
x y^{\prime }-n y&=x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.302 |
|
| \begin{align*}
\left (x^{3}+x \right ) y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.611 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| \begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.284 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.295 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.702 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x^{2}-1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.166 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.964 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.264 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.963 |
|
| \begin{align*}
x y^{\prime }&=y x +y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.933 |
|
| \begin{align*}
x y^{\prime }&=2 y \left (-1+y\right ) \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.881 |
|
| \begin{align*}
2 x y^{\prime }&=1-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.644 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.344 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
x y y^{\prime }&=\sqrt {y^{2}-9} \\
y \left ({\mathrm e}^{4}\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.737 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.694 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.926 |
|
| \begin{align*}
x^{2}-y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.314 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.348 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.914 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.927 |
|
| \begin{align*}
x y^{\prime }&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✓ |
5.405 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.147 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.691 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.762 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
57.701 |
|
| \begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.712 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.270 |
|
| \begin{align*}
1&=\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \\
\end{align*} |
[_exact, _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.575 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.815 |
|
| \begin{align*}
\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| \begin{align*}
\left (x -1-y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.826 |
|
| \begin{align*}
y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.488 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.873 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2}+9 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.055 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.585 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.499 |
|
| \begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
49.985 |
|
| \begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.625 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.806 |
|
| \begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
52.680 |
|
| \begin{align*}
x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.391 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.250 |
|
| \begin{align*}
x^{2}+y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.415 |
|
| \begin{align*}
\cos \left (x +y\right )-x \sin \left (x +y\right )&=x \sin \left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
6.687 |
|
| \begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.550 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.266 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.612 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.661 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.273 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.395 |
|
| \begin{align*}
y^{\prime }+\frac {x}{y}+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.109 |
|
| \begin{align*}
x y^{\prime }-y&=x \cot \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.414 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.148 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.197 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.812 |
|
| \begin{align*}
\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.165 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.327 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.072 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{x -y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.511 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.347 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.302 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
25.869 |
|
| \begin{align*}
x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.776 |
|
| \begin{align*}
2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.996 |
|
| \begin{align*}
y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.990 |
|
| \begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.899 |
|
| \begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
9.853 |
|
| \begin{align*}
x^{2}+y+y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.385 |
|
| \begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
71.989 |
|
| \begin{align*}
y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.300 |
|
| \begin{align*}
2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.349 |
|
| \begin{align*}
y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
19.643 |
|
| \begin{align*}
2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.619 |
|
| \begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| \begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.795 |
|
| \begin{align*}
x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
36.095 |
|
| \begin{align*}
2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
35.250 |
|
| \begin{align*}
1-\left (y-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.692 |
|
| \begin{align*}
\left (y^{3}+\frac {x}{y}\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
21.688 |
|
| \begin{align*}
1+\left (x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.803 |
|
| \begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| \begin{align*}
y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.283 |
|
| \begin{align*}
1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
8.401 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}}{x^{4} y+2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.342 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
64.366 |
|
| \begin{align*}
2 x y^{\prime }-y&=y^{\prime } \ln \left (y y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.044 |
|
| \begin{align*}
2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.717 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.113 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.398 |
|
| \begin{align*}
2 \sqrt {y x}-y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.336 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.973 |
|
| \begin{align*}
y-1-y x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.982 |
|
| \begin{align*}
2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
15.763 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.661 |
|
| \begin{align*}
y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
43.130 |
|
| \begin{align*}
y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.946 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.234 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.467 |
|
| \begin{align*}
x^{2} \left (x y^{\prime }-y\right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.810 |
|
| \begin{align*}
y^{4}+y x +\left (x y^{3}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
12.735 |
|
| \begin{align*}
x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.898 |
|
| \begin{align*}
y+\left (y x -x -y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.173 |
|
| \begin{align*}
y+2 y^{3} y^{\prime }&=\left (x +4 \ln \left (y\right ) y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.320 |
|
| \begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
15.757 |
|
| \begin{align*}
y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.652 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.297 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.239 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.378 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| \begin{align*}
y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.723 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.345 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y^{\prime }&=y \cot \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| \begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.616 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
y^{\prime }&=y \tan \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.226 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
y^{\prime }&=1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.560 |
|
| \begin{align*}
y^{\prime }&=\left (3+x -4 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.872 |
|
| \begin{align*}
y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
23.953 |
|
| \begin{align*}
y^{\prime }&=x y \left (y+3\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.349 |
|
| \begin{align*}
y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
5.754 |
|
| \begin{align*}
y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
5.757 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.109 |
|
| \begin{align*}
y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.178 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.872 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.682 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.282 |
|
| \begin{align*}
y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.262 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| \begin{align*}
y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| \begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.842 |
|
| \begin{align*}
y^{\prime }&=a x +b \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.212 |
|
| \begin{align*}
y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.820 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.319 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.717 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
21.488 |
|
| \begin{align*}
2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
15.806 |
|
| \begin{align*}
3 y^{\prime }&=x +\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.973 |
|
| \begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
97.709 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.625 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.071 |
|
| \begin{align*}
x y^{\prime }&=x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.066 |
|
| \begin{align*}
x y^{\prime }&=1+x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
x y^{\prime }&=x^{m}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
x y^{\prime }&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| \begin{align*}
x y^{\prime }&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.353 |
|
| \begin{align*}
x y^{\prime }&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x y^{\prime }&=1+x +a y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.378 |
|
| \begin{align*}
x y^{\prime }&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.083 |
|
| \begin{align*}
x y^{\prime }&=a +b \,x^{n}+c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.365 |
|
| \begin{align*}
x y^{\prime }+\left (b x +a \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.244 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.111 |
|
| \begin{align*}
x y^{\prime }+\left (-a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.134 |
|
| \begin{align*}
x y^{\prime }&=x^{2}+y \left (y+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| \begin{align*}
x y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.079 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.787 |
|
| \begin{align*}
x y^{\prime }+\left (-y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.570 |
|
| \begin{align*}
x y^{\prime }&=\left (-y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.580 |
|
| \begin{align*}
x y^{\prime }&=\left (y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.031 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.776 |
|
| \begin{align*}
x y^{\prime }+\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.353 |
|
| \begin{align*}
x y^{\prime }&=2 x -y+a \,x^{n} \left (x -y\right )^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.126 |
|
| \begin{align*}
x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.358 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.938 |
|
| \begin{align*}
x y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.365 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.107 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.597 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.555 |
|
| \begin{align*}
x y^{\prime }+2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.773 |
|
| \begin{align*}
x y^{\prime }&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.864 |
|
| \begin{align*}
x y^{\prime }+2 y&=\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.239 |
|
| \begin{align*}
x y^{\prime }+2 y&=-\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.200 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.394 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.266 |
|
| \begin{align*}
x y^{\prime }&=y+x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.493 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
51.185 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.256 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.612 |
|
| \begin{align*}
x y^{\prime }&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.565 |
|
| \begin{align*}
x y^{\prime }&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.345 |
|
| \begin{align*}
x y^{\prime }-y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.956 |
|
| \begin{align*}
x y^{\prime }&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.571 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.758 |
|
| \begin{align*}
x y^{\prime }+\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.762 |
|
| \begin{align*}
x y^{\prime }+x +\tan \left (x +y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.974 |
|
| \begin{align*}
x y^{\prime }&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.857 |
|
| \begin{align*}
x y^{\prime }&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.491 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.093 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.059 |
|
| \begin{align*}
x y^{\prime }&=\ln \left (y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.101 |
|
| \begin{align*}
x y^{\prime }&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.752 |
|
| \begin{align*}
x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
9.219 |
|
| \begin{align*}
x y^{\prime }&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.565 |
|
| \begin{align*}
x y^{\prime }&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
8.776 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.148 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.807 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.050 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.102 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b +c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.614 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=-b -c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.001 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.030 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.314 |
|
| \begin{align*}
\left (-x +a \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| \begin{align*}
2 x y^{\prime }&=2 x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
28.911 |
|
| \begin{align*}
2 x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.481 |
|
| \begin{align*}
2 x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.595 |
|
| \begin{align*}
2 x y^{\prime }&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.276 |
|
| \begin{align*}
2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.751 |
|
| \begin{align*}
2 x y^{\prime }+4 y+a -\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.902 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.914 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.704 |
|
| \begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.051 |
|
| \begin{align*}
3 x y^{\prime }&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.257 |
|
| \begin{align*}
x^{2} y^{\prime }&=a -y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.096 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.773 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.441 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.309 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (1+2 x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.255 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.750 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.834 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
28.460 |
|
| \begin{align*}
x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.341 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
7.020 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.078 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.733 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.107 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.326 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.783 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.046 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.242 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.062 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.478 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.639 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.553 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.324 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.744 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.959 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.471 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y^{2}-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.384 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y \left (2 x -y\right ) \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.349 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.882 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.738 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.584 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.575 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=a^{2}+3 y x -2 y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.000 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.516 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.717 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.038 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +2 \left (2-x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.631 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.299 |
|
| \begin{align*}
x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.095 |
|
| \begin{align*}
\left (x +a \right )^{2} y^{\prime }&=2 \left (x +a \right ) \left (b +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.116 |
|
| \begin{align*}
\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
27.814 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.625 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.452 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.760 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.782 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| \begin{align*}
2 x^{2} y^{\prime }+1+2 y x -x^{2} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.562 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime }&=4 x -\left (1+4 x \right ) y+y^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.914 |
|
| \begin{align*}
2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (2 x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
20.510 |
|
| \begin{align*}
a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
40.164 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.896 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.116 |
|
| \begin{align*}
x \left (a x +1\right ) y^{\prime }+a -y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.544 |
|
| \begin{align*}
x^{3} y^{\prime }&=b \,x^{2} y+a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| \begin{align*}
x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{4}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.657 |
|
| \begin{align*}
x^{3} y^{\prime }&=y \left (x^{2}+y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.696 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} \left (-1+y\right )+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.974 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.291 |
|
| \begin{align*}
x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.721 |
|
| \begin{align*}
x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.060 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.477 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.695 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.504 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.276 |
|
| \begin{align*}
x^{2} \left (1-x \right ) y^{\prime }&=x \left (2-x \right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.618 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.664 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.688 |
|
| \begin{align*}
x^{4} y^{\prime }&=\left (y+x^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.669 |
|
| \begin{align*}
x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
8.767 |
|
| \begin{align*}
x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.359 |
|
| \begin{align*}
\left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.629 |
|
| \begin{align*}
x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.292 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.817 |
|
| \begin{align*}
x^{5} y^{\prime }&=1-3 x^{4} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.532 |
|
| \begin{align*}
x^{n} y^{\prime }&=a +b \,x^{n -1} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.616 |
|
| \begin{align*}
x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.441 |
|
| \begin{align*}
x^{n} y^{\prime }&=a^{2} x^{2 n -2}+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
13.254 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.539 |
|
| \begin{align*}
y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
53.987 |
|
| \begin{align*}
\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }&=\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.209 |
|
| \begin{align*}
\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| \begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.751 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }&=a x \left (1+\ln \left (x \right )\right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.704 |
|
| \begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.969 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.451 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.542 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.144 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.658 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.753 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.849 |
|
| \begin{align*}
1-y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.594 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.924 |
|
| \begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.558 |
|
| \begin{align*}
\left (3-x -y\right ) y^{\prime }&=1+x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.369 |
|
| \begin{align*}
\left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.657 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.826 |
|
| \begin{align*}
\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.302 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.920 |
|
| \begin{align*}
\left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.540 |
|
| \begin{align*}
\left (1-3 x +y\right ) y^{\prime }&=2 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
176.494 |
|
| \begin{align*}
\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.398 |
|
| \begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
108.333 |
|
| \begin{align*}
\left (6-4 x -y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
39.344 |
|
| \begin{align*}
\left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.890 |
|
| \begin{align*}
\left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.557 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }&=4 y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.416 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.164 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.723 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.416 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.954 |
|
| \begin{align*}
\left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.073 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.781 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
41.601 |
|
| \begin{align*}
\left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.133 |
|
| \begin{align*}
\left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.451 |
|
| \begin{align*}
\left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.340 |
|
| \begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
86.715 |
|
| \begin{align*}
\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.233 |
|
| \begin{align*}
\left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
67.437 |
|
| \begin{align*}
\left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.172 |
|
| \begin{align*}
\left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.309 |
|
| \begin{align*}
\left (-3 y-2 x +5\right ) y^{\prime }+1-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.943 |
|
| \begin{align*}
\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.504 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.485 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.498 |
|
| \begin{align*}
\left (5+2 x -4 y\right ) y^{\prime }&=x -2 y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.281 |
|
| \begin{align*}
\left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.143 |
|
| \begin{align*}
4 \left (-x -y+1\right ) y^{\prime }+2-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.280 |
|
| \begin{align*}
\left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
68.718 |
|
| \begin{align*}
\left (6+3 x +5 y\right ) y^{\prime }&=2+x +7 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
198.494 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.580 |
|
| \begin{align*}
\left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
89.759 |
|
| \begin{align*}
3 \left (x +2 y\right ) y^{\prime }&=-2 y-x +1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.990 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
90.015 |
|
| \begin{align*}
\left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
40.445 |
|
| \begin{align*}
\left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.431 |
|
| \begin{align*}
\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.876 |
|
| \begin{align*}
\left (3+9 x +21 y\right ) y^{\prime }&=45+7 x -5 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.658 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.843 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.737 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+b x +a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.021 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }&=b x +a y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.991 |
|
| \begin{align*}
\left (a_{2} +b x +c_{2} y\right ) y^{\prime }+a_{1} +b_{1} x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
97.866 |
|
| \begin{align*}
\left (a_{2} +b_{2} x +c_{2} y\right ) y^{\prime }&=a_{1} +b_{1} x +c_{1} y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
96.440 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.709 |
|
| \begin{align*}
x y y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.530 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.833 |
|
| \begin{align*}
x y y^{\prime }+x^{4}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.169 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.667 |
|
| \begin{align*}
x y y^{\prime }+2 x^{2}-2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
22.504 |
|
| \begin{align*}
x y y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| \begin{align*}
x y y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
14.744 |
|
| \begin{align*}
x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.790 |
|
| \begin{align*}
x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.794 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
70.733 |
|
| \begin{align*}
x \left (4+y\right ) y^{\prime }&=2 x +2 y+y^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
35.362 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
125.414 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
80.546 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.326 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.129 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.029 |
|
| \begin{align*}
x \left (2 x +y\right ) y^{\prime }&=x^{2}+y x -y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.600 |
|
| \begin{align*}
x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
123.256 |
|
| \begin{align*}
x \left (y+x^{3}\right ) y^{\prime }&=\left (x^{3}-y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
96.493 |
|
| \begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=\left (2 x^{3}-y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
90.189 |
|
| \begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=6 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
85.961 |
|
| \begin{align*}
\left (x +a \right ) \left (x +b \right ) y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.252 |
|
| \begin{align*}
2 x y y^{\prime }+a +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.499 |
|
| \begin{align*}
2 x y y^{\prime }&=a x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.964 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.068 |
|
| \begin{align*}
2 x y y^{\prime }&=4 x^{2} \left (2 x +1\right )+y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.647 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
57.220 |
|
| \begin{align*}
x \left (x +2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
43.512 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.112 |
|
| \begin{align*}
2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.785 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
70.752 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.523 |
|
| \begin{align*}
a x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.247 |
|
| \begin{align*}
a x y y^{\prime }+x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.010 |
|
| \begin{align*}
x \left (a +b y\right ) y^{\prime }&=c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.437 |
|
| \begin{align*}
x \left (x -a y\right ) y^{\prime }&=y \left (y-a x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
37.050 |
|
| \begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
83.664 |
|
| \begin{align*}
x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
55.773 |
|
| \begin{align*}
x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
87.181 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.641 |
|
| \begin{align*}
x \left (1-2 y x \right ) y^{\prime }+y \left (1+2 y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.126 |
|
| \begin{align*}
x \left (1+2 y x \right ) y^{\prime }+\left (2+3 y x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
49.720 |
|
| \begin{align*}
x \left (1+2 y x \right ) y^{\prime }+\left (1+2 y x -x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
63.033 |
|
| \begin{align*}
x^{2} \left (x -2 y\right ) y^{\prime }&=2 x^{3}-4 x y^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
87.370 |
|
| \begin{align*}
2 \left (x +1\right ) x y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.227 |
|
| \begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.845 |
|
| \begin{align*}
x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 y x +2 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.842 |
|
| \begin{align*}
\left (1-x^{3} y\right ) y^{\prime }&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
69.137 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+a +3 x^{2} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.646 |
|
| \begin{align*}
x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
243.663 |
|
| \begin{align*}
8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
94.512 |
|
| \begin{align*}
x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.490 |
|
| \begin{align*}
3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.707 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.639 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.928 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.967 |
|
| \begin{align*}
\left (1-x^{2}+y^{2}\right ) y^{\prime }&=-y^{2}+x^{2}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
4.915 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.198 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.152 |
|
| \begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }&=4 x^{3} y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.840 |
|
| \begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| \begin{align*}
\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
7.032 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.965 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.620 |
|
| \begin{align*}
\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.311 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.748 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.697 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.484 |
|
| \begin{align*}
\left (a +b +x +y\right )^{2} y^{\prime }&=2 \left (y+a \right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
10.787 |
|
| \begin{align*}
\left (3 x +y\right )^{2} y^{\prime }&=4 \left (3 x +2 y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.755 |
|
| \begin{align*}
\left (1-3 x -y\right )^{2} y^{\prime }&=\left (-2 y+1\right ) \left (3-6 x -4 y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.933 |
|
| \begin{align*}
\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.954 |
|
| \begin{align*}
\left (1-3 x +2 y\right )^{2} y^{\prime }&=\left (4+2 x -3 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
16.602 |
|
| \begin{align*}
\left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.651 |
|
| \begin{align*}
\left (x^{2}+y x +a y^{2}\right ) y^{\prime }&=a \,x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
108.831 |
|
| \begin{align*}
\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.385 |
|
| \begin{align*}
\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
145.987 |
|
| \begin{align*}
x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
18.645 |
|
| \begin{align*}
x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (-y^{2}+x^{2}+1\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
13.083 |
|
| \begin{align*}
x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
21.872 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.632 |
|
| \begin{align*}
\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
12.956 |
|
| \begin{align*}
x \left (y+a \right )^{2} y^{\prime }&=b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.602 |
|
| \begin{align*}
x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
67.832 |
|
| \begin{align*}
x \left (x^{2}-y x -y^{2}\right ) y^{\prime }&=\left (x^{2}+y x -y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.581 |
|
| \begin{align*}
x \left (x^{2}+a x y+y^{2}\right ) y^{\prime }&=\left (x^{2}+b x y+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.852 |
|
| \begin{align*}
x \left (x^{2}-2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.772 |
|
| \begin{align*}
x \left (x^{2}+2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.041 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.059 |
|
| \begin{align*}
x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.797 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=2 x -y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.994 |
|
| \begin{align*}
x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
11.555 |
|
| \begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| \begin{align*}
x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.771 |
|
| \begin{align*}
x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.397 |
|
| \begin{align*}
x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.355 |
|
| \begin{align*}
\left (1-x^{2} y^{2}\right ) y^{\prime }&=x y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.039 |
|
| \begin{align*}
x \left (1+x y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.285 |
|
| \begin{align*}
x \left (1+x y^{2}\right ) y^{\prime }&=\left (2-3 x y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
50.504 |
|
| \begin{align*}
x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.274 |
|
| \begin{align*}
x \left (-y x +1\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.730 |
|
| \begin{align*}
\left (1-y^{2} x^{4}\right ) y^{\prime }&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
15.575 |
|
| \begin{align*}
\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.789 |
|
| \begin{align*}
\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.866 |
|
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.213 |
|
| \begin{align*}
x \left (x -y^{3}\right ) y^{\prime }&=\left (3 x +y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
17.237 |
|
| \begin{align*}
x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=\left (2 x^{3}-x^{2} y+y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
418.898 |
|
| \begin{align*}
x \left (2 x^{3}-y^{3}\right ) y^{\prime }&=\left (x^{3}-2 y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
131.046 |
|
| \begin{align*}
x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime }&=\left (3 x^{2}+y^{2}\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.197 |
|
| \begin{align*}
x \left (x^{3}-2 y^{3}\right ) y^{\prime }&=\left (2 x^{3}-y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
113.617 |
|
| \begin{align*}
x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
24.353 |
|
| \begin{align*}
x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.978 |
|
| \begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.391 |
|
| \begin{align*}
\left (x^{3}-y^{4}\right ) y^{\prime }&=3 x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
19.623 |
|
| \begin{align*}
\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime }&=a^{2} x y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
12.599 |
|
| \begin{align*}
2 \left (x -y^{4}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.455 |
|
| \begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
55.118 |
|
| \begin{align*}
2 x \left (x^{3}+y^{4}\right ) y^{\prime }&=\left (x^{3}+2 y^{4}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.973 |
|
| \begin{align*}
x \left (1-x^{2} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.348 |
|
| \begin{align*}
\left (x^{2}-y^{5}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.627 |
|
| \begin{align*}
x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.935 |
|
| \begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.866 |
|
| \begin{align*}
x \left (a +x y^{n}\right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
24.711 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.042 |
|
| \begin{align*}
y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
56.276 |
|
| \begin{align*}
\left (x -2 \sqrt {y x}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.964 |
|
| \begin{align*}
x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
7.841 |
|
| \begin{align*}
x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
101.317 |
|
| \begin{align*}
x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.039 |
|
| \begin{align*}
\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }&=x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.463 |
|
| \begin{align*}
\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.257 |
|
| \begin{align*}
x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
62.564 |
|
| \begin{align*}
\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.634 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
73.582 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x +y \left (y+1\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
36.935 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
36.586 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.682 |
|
| \begin{align*}
\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
47.555 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
174.573 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
52.244 |
|
| \begin{align*}
{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
323.892 |
|
| \begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1458.479 |
|
| \begin{align*}
2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
61.622 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+x y^{\prime }+a&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
13.802 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.982 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.299 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
13.830 |
|
| \begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.051 |
|
| \begin{align*}
y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
12.109 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.753 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
67.729 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.369 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.763 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
48.891 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.944 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.625 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.234 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
93.951 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
58.004 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.329 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.338 |
|
| \begin{align*}
2 x -y+1+\left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
72.880 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
143.994 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.502 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.619 |
|
| \begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.214 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.351 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
58.749 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.658 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
65.674 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
176.794 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
124.164 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
43.831 |
|
| \begin{align*}
\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
134.820 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.544 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.937 |
|
| \begin{align*}
2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.805 |
|
| \begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
186.047 |
|
| \begin{align*}
\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.798 |
|
| \begin{align*}
y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
123.645 |
|
| \begin{align*}
2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.250 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x -\sin \left (\frac {y}{x}\right ) y+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
39.883 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
74.717 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=x y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
59.353 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.149 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.686 |
|
| \begin{align*}
x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.892 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.400 |
|
| \begin{align*}
x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.086 |
|
| \begin{align*}
x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
68.105 |
|
| \begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.970 |
|
| \begin{align*}
7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.941 |
|
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.659 |
|
| \begin{align*}
x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.704 |
|
| \begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.375 |
|
| \begin{align*}
x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
38.230 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
107.801 |
|
| \begin{align*}
y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.803 |
|
| \begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.154 |
|
| \begin{align*}
y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
38.673 |
|
| \begin{align*}
x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
13.109 |
|
| \begin{align*}
y-\left (x^{2}+y^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.566 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.448 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.763 |
|
| \begin{align*}
x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.754 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| \begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.063 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.387 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.484 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.345 |
|
| \begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.606 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.576 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
32.737 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
46.384 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y-1&=\left (x +1\right ) \sqrt {y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.682 |
|
| \begin{align*}
{\mathrm e}^{y} \left (y^{\prime }+1\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.392 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.859 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.513 |
|
| \begin{align*}
\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
63.796 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.535 |
|
| \begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
11.151 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.592 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}+2 y-1\right )^{{2}/{3}}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.521 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{\prime }+a y&=k \,{\mathrm e}^{b x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.685 |
|
| \begin{align*}
x y^{\prime }-y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.734 |
|
| \begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| \begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.299 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.667 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.749 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.357 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.370 |
|
| \begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.420 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.586 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| \begin{align*}
2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
93.477 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| \begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| \begin{align*}
a x y^{3}+b y^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.938 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.605 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.915 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.376 |
|
| \begin{align*}
a x y^{\prime }+2 y&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.767 |
|
| \begin{align*}
y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.275 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.299 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.688 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| \begin{align*}
\left (y x +x \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.238 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.891 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+3 y^{3}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.033 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }+x +y+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.441 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.796 |
|
| \begin{align*}
y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.332 |
|
| \begin{align*}
y^{2}-y x +\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.260 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.272 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.282 |
|
| \begin{align*}
y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.779 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.376 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.356 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=\frac {1}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.275 |
|
| \begin{align*}
y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
y+2 x -x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }-x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.533 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.733 |
|
| \begin{align*}
3 x^{2} y+x^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \\
y \left (2\right ) &= 6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| \begin{align*}
x y^{\prime }&=y x +y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.523 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| \begin{align*}
y^{\prime }-\sin \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
x y^{\prime }&=\frac {1}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \begin{align*}
x^{\prime }&=3 x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.125 |
|
| \begin{align*}
x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.695 |
|
| \begin{align*}
y^{\prime }&=\frac {\sec \left (y\right )^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.366 |
|
| \begin{align*}
\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.526 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\
y \left (0\right ) &= \sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
6.953 |
|
| \begin{align*}
y^{\prime }&=x^{3} \left (1-y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \begin{align*}
x^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.228 |
|
| \begin{align*}
y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.530 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (y+1\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.095 |
|
| \begin{align*}
\sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.421 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
25.469 |
|
| \begin{align*}
y^{\prime }&=2 y-2 y t \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
y^{\prime }&=\left (x -3\right ) \left (y+1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.235 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.434 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.641 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=y t -y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| \begin{align*}
3 r&=r^{\prime }-\theta ^{3} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.446 |
|
| \begin{align*}
y^{\prime }-y-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+2 x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {1}{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
t +y+1-y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| \begin{align*}
y x^{\prime }+2 x&=5 y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= {\mathrm e}-1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= {\frac {4}{3}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}+2&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| \begin{align*}
\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.734 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.136 |
|
| \begin{align*}
x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.485 |
|
| \begin{align*}
x^{{10}/{3}}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| \begin{align*}
\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.014 |
|
| \begin{align*}
{\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.900 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.011 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.532 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.973 |
|
| \begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.434 |
|
| \begin{align*}
x^{4}-x +y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.513 |
|
| \begin{align*}
2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.747 |
|
| \begin{align*}
3 y+2 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
34.831 |
|
| \begin{align*}
2 t x x^{\prime }+t^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.142 |
|
| \begin{align*}
\left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.270 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.155 |
|
| \begin{align*}
\left (t +x+2\right ) x^{\prime }+3 t -x-6&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.804 |
|
| \begin{align*}
-y+t y^{\prime }&=\sqrt {y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.010 |
|
| \begin{align*}
y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.808 |
|
| \begin{align*}
\cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| \begin{align*}
3 x^{2}-y^{2}-\left (y x -\frac {x^{3}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.227 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.288 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.838 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.296 |
|
| \begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.026 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.846 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.086 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+5\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.124 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.958 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.407 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.967 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.698 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.793 |
|
| \begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.905 |
|
| \begin{align*}
-4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
137.719 |
|
| \begin{align*}
2 x -y+\left (4 x +y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
21.344 |
|
| \begin{align*}
2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.805 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\cos \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.601 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.072 |
|
| \begin{align*}
y^{\prime }&=x^{3} \left (-x +y\right )^{2}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.400 |
|
| \begin{align*}
y^{\prime }-4 y&=32 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.193 |
|
| \begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| \begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| \begin{align*}
x^{2}+y^{2}+3 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
x^{\prime }&=1+\cos \left (t -x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.772 |
|
| \begin{align*}
y^{3}+4 y \,{\mathrm e}^{x}+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.580 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\sin \left (2 x \right ) x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| \begin{align*}
y^{\prime }&=2-\sqrt {2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.136 |
|
| \begin{align*}
y^{\prime }&=\left (2 x +y-1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.918 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.864 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \begin{align*}
y-2 x -1+\left (x +y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.163 |
|
| \begin{align*}
2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.506 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.263 |
|
| \begin{align*}
y \left (x -y-2\right )+x \left (-x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
16.276 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| \begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.777 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.425 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.488 |
|
| \begin{align*}
t +x+3+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.310 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| \begin{align*}
2 x -y+\left (-3+x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.668 |
|
| \begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.286 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.260 |
|
| \begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.728 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x -x +1&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| \begin{align*}
y^{\prime }+y&=\left (x +1\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
y^{\prime }+\frac {y}{1-x}+2 x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.473 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.714 |
|
| \begin{align*}
3 x y^{\prime }+y+x^{2} y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.567 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}-x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.768 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.594 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.820 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.904 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.744 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.067 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.618 |
|
| \begin{align*}
x y^{\prime }+3 y&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.151 |
|
| \begin{align*}
x \left (-3+y\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.925 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| \begin{align*}
x^{3}+\left (y+1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.748 |
|
| \begin{align*}
y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.576 |
|
| \begin{align*}
x^{3}+y^{3}&=3 x y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| \begin{align*}
y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.953 |
|
| \begin{align*}
\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=y^{3}+3 x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
211.522 |
|
| \begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.849 |
|
| \begin{align*}
x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.071 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.537 |
|
| \begin{align*}
\left (y x +1\right ) y+x \left (1+y x +x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.123 |
|
| \begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.965 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
13.701 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x -1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}-x y y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
22.902 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.526 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.029 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.213 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.435 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
y^{\prime }+x +x y^{2}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
4.496 |
|
| \begin{align*}
x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.634 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.402 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.390 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.371 |
|
| \begin{align*}
4 y+x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.162 |
|
| \begin{align*}
1+2 y+\left (-x^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.070 |
|
| \begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.429 |
|
| \begin{align*}
1+y-\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| \begin{align*}
x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
37.159 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.648 |
|
| \begin{align*}
y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.653 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.900 |
|
| \begin{align*}
1+2 y-\left (4-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.711 |
|
| \begin{align*}
x +2 y+\left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.145 |
|
| \begin{align*}
2 x y^{\prime }-2 y&=\sqrt {x^{2}+4 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.036 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.290 |
|
| \begin{align*}
y^{2}-x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| \begin{align*}
y \left (1+2 y x \right )+x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
50.445 |
|
| \begin{align*}
1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.862 |
|
| \begin{align*}
x^{3}+y^{3}+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.563 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.356 |
|
| \begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.503 |
|
| \begin{align*}
y^{\prime }&=-2 \left (2 x +3 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.639 |
|
| \begin{align*}
y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.983 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.303 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.366 |
|
| \begin{align*}
x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.641 |
|
| \begin{align*}
1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.259 |
|
| \begin{align*}
y^{\prime }+y&=2 x +2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
y^{\prime }-y&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
-3 y-\left (x -2\right ) {\mathrm e}^{x}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| \begin{align*}
x y^{\prime }+y-x^{3} y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| \begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.076 |
|
| \begin{align*}
2+y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| \begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.487 |
|
| \begin{align*}
2 y^{5} x -y+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.902 |
|
| \begin{align*}
x y^{\prime }&=2 y+{\mathrm e}^{x} x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.133 |
|
| \begin{align*}
x y^{\prime }&=1-x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.699 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.864 |
|
| \begin{align*}
y^{2}-1+x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.703 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.560 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.395 |
|
| \begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.932 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.468 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.448 |
|
| \begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.339 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.128 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.925 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.251 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.459 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
19.694 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.824 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.210 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.086 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.181 |
|
| \begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.375 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.107 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.430 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.647 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.951 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.400 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.392 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.060 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.840 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.626 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.951 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (1\right ) &= {\frac {5}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.189 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.636 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.645 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
x y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.218 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.404 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.510 |
|
| \begin{align*}
n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.948 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.831 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-1}{x^{2}-1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
5.589 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.886 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.072 |
|
| \begin{align*}
\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
5.365 |
|
| \begin{align*}
x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.928 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\
y \left (4\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\
y \left (-2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.533 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
16.156 |
|
| \begin{align*}
y^{\prime }&=\frac {1+3 x}{2 y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.496 |
|
| \begin{align*}
{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.788 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.670 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.046 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.257 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.043 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.575 |
|
| \begin{align*}
y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.635 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.049 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.112 |
|
| \begin{align*}
y^{\prime }&=2 y+x^{2}+5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.159 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.794 |
|
| \begin{align*}
4 y+x y^{\prime }&=x^{3}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.867 |
|
| \begin{align*}
y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.239 |
|
| \begin{align*}
\left (x +2\right )^{2} y^{\prime }&=5-8 y-4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
p^{\prime }+2 t p&=p+4 t -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
x y^{\prime }+\left (1+3 x \right ) y&={\mathrm e}^{-3 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.406 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| \begin{align*}
y^{\prime }&=x +5 y \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.627 |
|
| \begin{align*}
y^{\prime }&=2 x -3 y \\
y \left (0\right ) &= {\frac {1}{3}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \begin{align*}
x y^{\prime }+y&=1+4 x \\
y \left (1\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.649 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=2 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| \begin{align*}
y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.741 |
|
| \begin{align*}
1&=\left (x +y^{2}\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.353 |
|
| \begin{align*}
2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.232 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.756 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.266 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.917 |
|
| \begin{align*}
x y y^{\prime }&=\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.274 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.004 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.943 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.037 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| \begin{align*}
\frac {y}{x -1}+\frac {x y^{\prime }}{y+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.169 |
|
| \begin{align*}
\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.009 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) \left (x +1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.543 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.947 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.479 |
|
| \begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.438 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| \begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.156 |
|
| \begin{align*}
y^{\prime }+y&=2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| \begin{align*}
y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.694 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.144 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.703 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.381 |
|
| \begin{align*}
y-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.259 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.126 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
41.555 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.326 |
|
| \begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.282 |
|
| \begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.540 |
|
| \begin{align*}
x y^{\prime }&=y \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.335 |
|
| \begin{align*}
y+\sqrt {y x}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.392 |
|
| \begin{align*}
x y^{\prime }-\sqrt {x^{2}-y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.678 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.178 |
|
| \begin{align*}
x y^{\prime }-y&=y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.125 |
|
| \begin{align*}
y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
69.950 |
|
| \begin{align*}
x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.126 |
|
| \begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
77.598 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.361 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.842 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.726 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.088 |
|
| \begin{align*}
x y^{\prime }&=y \ln \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.551 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.356 |
|
| \begin{align*}
y^{\prime }+\frac {x +2 y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.204 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.715 |
|
| \begin{align*}
x y^{\prime }&=x +\frac {y}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
40.325 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.535 |
|
| \begin{align*}
2 x -4 y+6+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
34.211 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
62.911 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.562 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.188 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.322 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.425 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.802 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.151 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
83.615 |
|
| \begin{align*}
2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.553 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.214 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.962 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
x y^{\prime }-2 \sqrt {y x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.566 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.447 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.833 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.241 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| \begin{align*}
y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.332 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.504 |
|
| \begin{align*}
\left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.730 |
|
| \begin{align*}
\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
30.527 |
|
| \begin{align*}
\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.250 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.046 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.087 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}-y^{2}}\, y^{\prime } \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.948 |
|
| \begin{align*}
x +y y^{\prime }+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.993 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2}+x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.631 |
|
| \begin{align*}
y+3 y^{\prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.731 |
|
| \begin{align*}
y^{\prime }+i y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.445 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{3}-1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.779 |
|
| \begin{align*}
y^{\prime }+y \,{\mathrm e}^{x}&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.674 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.063 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.756 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2}-4 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
8.346 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.635 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.178 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.809 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.801 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.145 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y+1}{x -2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.260 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.236 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.361 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.090 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.972 |
|
| \begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {1-x^{2} y^{2}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
34.799 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.490 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.060 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.533 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.710 |
|
| \begin{align*}
\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.939 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}}{1-x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
34.647 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.411 |
|
| \begin{align*}
y^{\prime }&=4 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.736 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.616 |
|
| \begin{align*}
\ln \left (y\right ) y-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.771 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| \begin{align*}
x y y^{\prime }&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.548 |
|
| \begin{align*}
x y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.135 |
|
| \begin{align*}
y^{2} y^{\prime }&=x +2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.277 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.135 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.801 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.635 |
|
| \begin{align*}
-x y^{\prime }+y&=y^{\prime } y^{2} {\mathrm e}^{y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.229 |
|
| \begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
11.924 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2} y+y \ln \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
64.098 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \begin{align*}
\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}&=1 \\
\end{align*} |
[_exact, _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.443 |
|
| \begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.417 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
9.172 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.487 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.155 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.238 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.771 |
|
| \begin{align*}
x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.493 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.744 |
|
| \begin{align*}
x y^{\prime }&=2 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.120 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.569 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.839 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.747 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.139 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.318 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.161 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
267.683 |
|
| \begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.053 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.514 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.405 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
65.319 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.153 |
|
| \begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.589 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.891 |
|
| \begin{align*}
y^{\prime }&=\frac {y \tan \left (\frac {y}{x}\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.908 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
22.400 |
|
| \begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.796 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.766 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.948 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.070 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.743 |
|
| \begin{align*}
x y^{\prime }-y&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.492 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \\
y \left (-1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.951 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.926 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.320 |
|
| \begin{align*}
2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.325 |
|
| \begin{align*}
\frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.963 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.616 |
|
| \begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.616 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.513 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.579 |
|
| \begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.912 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.665 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
6.827 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.426 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.085 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.122 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
8.431 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.559 |
|
| \begin{align*}
y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
121.228 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y}+x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
105.909 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.136 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.928 |
|
| \begin{align*}
2 t +3 x+\left (x+2\right ) x^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.570 |
|
| \begin{align*}
y^{2}+\frac {2}{x}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.474 |
|
| \begin{align*}
y y^{\prime }-y&=x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.649 |
|
| \begin{align*}
y^{\prime }&=-4 \sin \left (x -y\right )-4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.362 |
|
| \begin{align*}
y^{\prime }+\sin \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
122.758 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.099 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.767 |
|
| \begin{align*}
x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.288 |
|
| \begin{align*}
y^{\prime }&=a x y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.480 |
|
| \begin{align*}
y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
c y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
c y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.848 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.260 |
|
| \begin{align*}
y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.938 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.796 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \begin{align*}
y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.603 |
|
| \begin{align*}
y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.695 |
|
| \begin{align*}
y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.186 |
|
| \begin{align*}
y^{\prime }-\left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.406 |
|
| \begin{align*}
y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.733 |
|
| \begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.121 |
|
| \begin{align*}
a x y^{3}+b y^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
5.070 |
|
| \begin{align*}
y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
4.417 |
|
| \begin{align*}
y^{\prime }-a \sqrt {y}-b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
4.872 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.086 |
|
| \begin{align*}
y^{\prime }-\cos \left (b x +a y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
y^{\prime }-f \left (a x +b y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| \begin{align*}
y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.535 |
|
| \begin{align*}
x y^{\prime }-y-\frac {x}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.379 |
|
| \begin{align*}
x y^{\prime }-y-x^{2} \sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| \begin{align*}
x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.718 |
|
| \begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.197 |
|
| \begin{align*}
x y^{\prime }-y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.477 |
|
| \begin{align*}
x y^{\prime }+a y^{2}-y+b \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.364 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.595 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y-a \,x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.166 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.428 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.630 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.350 |
|
| \begin{align*}
x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.751 |
|
| \begin{align*}
x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.349 |
|
| \begin{align*}
x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.305 |
|
| \begin{align*}
x y^{\prime }-\ln \left (y\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.042 |
|
| \begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.837 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.607 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.966 |
|
| \begin{align*}
x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.833 |
|
| \begin{align*}
x y^{\prime }-y f \left (y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.160 |
|
| \begin{align*}
x y^{\prime }-y f \left (x^{a} y^{b}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
3.398 |
|
| \begin{align*}
2 x y^{\prime }-y-2 x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.679 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.857 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.656 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.197 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.134 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.416 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.205 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.357 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.528 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.287 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.523 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.537 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.246 |
|
| \begin{align*}
x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.742 |
|
| \begin{align*}
3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.877 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.681 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.707 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.240 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.361 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.294 |
|
| \begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.381 |
|
| \begin{align*}
x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.105 |
|
| \begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.330 |
|
| \begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.952 |
|
| \begin{align*}
x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.481 |
|
| \begin{align*}
x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.977 |
|
| \begin{align*}
x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
10.158 |
|
| \begin{align*}
x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.694 |
|
| \begin{align*}
\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.553 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \begin{align*}
y y^{\prime }+a y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.286 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.683 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime }-y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
23.541 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }-y+2 x +3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.993 |
|
| \begin{align*}
\left (y+2 x -2\right ) y^{\prime }-y+x +1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.249 |
|
| \begin{align*}
\left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.854 |
|
| \begin{align*}
\left (y-x^{2}\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.921 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.489 |
|
| \begin{align*}
\left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.391 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }-y-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.015 |
|
| \begin{align*}
\left (2 y-6 x \right ) y^{\prime }-y+3 x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.893 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.477 |
|
| \begin{align*}
\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.654 |
|
| \begin{align*}
\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.461 |
|
| \begin{align*}
\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
52.737 |
|
| \begin{align*}
\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| \begin{align*}
\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma &=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
50.236 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \begin{align*}
x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
16.214 |
|
| \begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }-y \left (x +y\right )-b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.573 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.955 |
|
| \begin{align*}
2 x y y^{\prime }-y^{2}+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.938 |
|
| \begin{align*}
2 x y y^{\prime }-y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.817 |
|
| \begin{align*}
2 x y y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.844 |
|
| \begin{align*}
\left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
63.178 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.895 |
|
| \begin{align*}
\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.800 |
|
| \begin{align*}
\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
10.255 |
|
| \begin{align*}
x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
26.312 |
|
| \begin{align*}
x \left (y x -3\right ) y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
48.121 |
|
| \begin{align*}
\left (x +2 x^{2} y\right ) y^{\prime }-x^{2} y^{3}+2 x y^{2}+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
28.196 |
|
| \begin{align*}
\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
50.437 |
|
| \begin{align*}
\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.421 |
|
| \begin{align*}
2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
53.202 |
|
| \begin{align*}
\left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}}&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
✗ |
37.268 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.456 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.478 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.541 |
|
| \begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.278 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.491 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.177 |
|
| \begin{align*}
\left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.238 |
|
| \begin{align*}
\left (x^{2}+4 y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.072 |
|
| \begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.368 |
|
| \begin{align*}
\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
10.523 |
|
| \begin{align*}
\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.330 |
|
| \begin{align*}
\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
170.814 |
|
| \begin{align*}
\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
5.338 |
|
| \begin{align*}
\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.020 |
|
| \begin{align*}
x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.296 |
|
| \begin{align*}
x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.792 |
|
| \begin{align*}
x \left (y^{2}+y x -x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.055 |
|
| \begin{align*}
x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.494 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.746 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.360 |
|
| \begin{align*}
\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
6.569 |
|
| \begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.272 |
|
| \begin{align*}
\left (x^{2}+6 x y^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.274 |
|
| \begin{align*}
\left (x^{2} y^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.628 |
|
| \begin{align*}
\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
10.212 |
|
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.096 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
103.984 |
|
| \begin{align*}
\left (2 x^{2} y^{3}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.797 |
|
| \begin{align*}
y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
139.227 |
|
| \begin{align*}
y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
44.650 |
|
| \begin{align*}
a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.194 |
|
| \begin{align*}
y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.475 |
|
| \begin{align*}
\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.509 |
|
| \begin{align*}
\left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
17.472 |
|
| \begin{align*}
\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
59.385 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \begin{align*}
\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
89.131 |
|
| \begin{align*}
\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.416 |
|
| \begin{align*}
x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (x y^{\prime }+y\right )+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
15.047 |
|
| \begin{align*}
\left (-1+2 x +\ln \left (y\right )\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.825 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.260 |
|
| \begin{align*}
\left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
8.800 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.518 |
|
| \begin{align*}
\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.756 |
|
| \begin{align*}
\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
26.139 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
43.134 |
|
| \begin{align*}
\left (x y^{\prime }+y+2 x \right )^{2}-4 y x -4 x^{2}-4 a&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.394 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x +y \left (y+1\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
6.784 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.555 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
135.895 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
11.822 |
|
| \begin{align*}
\left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
21.191 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✗ |
✓ |
✗ |
22.052 |
|
| \begin{align*}
{y^{\prime }}^{4}-4 y \left (x y^{\prime }-2 y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
162.135 |
|
| \begin{align*}
{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
5.224 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.004 |
|
| \begin{align*}
a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
29.124 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+x y^{\prime }+a y+b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.812 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| \begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.617 |
|
| \begin{align*}
y^{\prime }&=F \left (\frac {y}{x +a}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.202 |
|
| \begin{align*}
y^{\prime }&=2 x +F \left (y-x^{2}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.202 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.515 |
|
| \begin{align*}
y^{\prime }&=F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.559 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| \begin{align*}
y^{\prime }&=\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.484 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.235 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{-y+F \left (x^{2}+y^{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.763 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.044 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.924 |
|
| \begin{align*}
y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
3.654 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +F \left (x^{2}+y^{2}\right )}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.381 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
4.416 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.203 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.508 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.232 |
|
| \begin{align*}
y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
1.315 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x -y+F \left (x \left (x +y\right )\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.043 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.088 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (a -1\right ) \left (a +1\right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.698 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| \begin{align*}
y^{\prime }&=-\frac {-x^{2}+2 x^{3} y-F \left (\left (y x -1\right ) x \right )}{x^{4}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.369 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.089 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+\sqrt {x}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
23.837 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
22.167 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y+x^{{3}/{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
35.656 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
80.438 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.606 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.209 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
34.607 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.546 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.661 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.466 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
11.484 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.620 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+x^{2}\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.403 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.761 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+x \right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.888 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.939 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.007 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.808 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.544 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.140 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
9.727 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.034 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.174 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.011 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.330 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.994 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.319 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.319 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.472 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.830 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.717 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.064 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.286 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.443 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.542 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
3.594 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
3.670 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
3.350 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
6.798 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| \begin{align*}
y^{\prime }&=\frac {-a b y+b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.024 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.748 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.960 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.140 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.207 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
38.889 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{y+2 y^{4} a -16 a^{2} x y^{2}+32 a^{3} x^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.381 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
37.100 |
|
| \begin{align*}
y^{\prime }&=\frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+x^{2} \ln \left (2 x \right )}{\ln \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.558 |
|
| \begin{align*}
y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.027 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.290 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
54.206 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.934 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.268 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.056 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.718 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.786 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
69.211 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.506 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.613 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.306 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
5.310 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.242 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.661 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.279 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.385 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.126 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.803 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+y x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
71.059 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.337 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.951 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.749 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
4.040 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.605 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.244 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
7.638 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.166 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.220 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 x y \ln \left (x \right )+\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
26.126 |
|
| \begin{align*}
y^{\prime }&=-\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
56.125 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.985 |
|
| \begin{align*}
y^{\prime }&=-\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✗ |
✓ |
✗ |
4.645 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
14.178 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y x +1\right )}{x \left (y x +1-y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
19.227 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+x^{3} y^{4}\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.151 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.449 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| \begin{align*}
y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
28.817 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
11.031 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x +2 y x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
84.898 |
|
| \begin{align*}
y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.007 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+y^{2}-2 x y \ln \left (x \right )+x^{2} \ln \left (x \right )^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.209 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.777 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y x +x y^{3}+x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.816 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x -1+x^{3} y^{4}\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.060 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
24.663 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x y^{3}+2 x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.550 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.697 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.005 |
|
| \begin{align*}
y^{\prime }&=\frac {b^{3}+y^{2} b^{3}+2 a \,b^{2} x y+a^{2} b \,x^{2}+b^{3} y^{3}+3 a \,b^{2} x y^{2}+3 a^{2} b \,x^{2} y+a^{3} x^{3}}{b^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.109 |
|
| \begin{align*}
y^{\prime }&=\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.130 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.240 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
15.392 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
2.770 |
|
| \begin{align*}
y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
2.531 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 y x +2 x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.482 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2} \left (x^{2} y-2 x -2 y x +y\right )}{2 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
10.376 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 x^{2} y^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.350 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 a}{-y-2 a -2 y^{4} a +16 a^{2} x y^{2}-32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.656 |
|
| \begin{align*}
y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.378 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
8.705 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +x^{4} y^{3}}{x^{2} \left (x^{2} y-x +1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
20.512 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{-y+1+y^{4}+2 x^{2} y^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.211 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{-\frac {2}{x^{2}-y^{2}-1}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{-\frac {2}{x^{2}-y^{2}-1}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.220 |
|
| \begin{align*}
y^{\prime }&=\frac {x +1+y^{4}-2 x^{2} y^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 y^{2} x^{4}-x^{6}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.481 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
5.218 |
|
| \begin{align*}
y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.257 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
9.352 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.549 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right )}{4 y+y^{4} a^{2}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 x^{2} y^{2}-x^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.586 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
2.997 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
7.492 |
|
| \begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
11.541 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.002 |
|
| \begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
11.746 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}} \left (x -y+\sqrt {y}\right )}{x y^{{3}/{2}}-y^{{5}/{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
11.883 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y^{2}+y^{{3}/{2}}+x^{2} \sqrt {y}-2 x y^{{3}/{2}}+y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
6.263 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.134 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.392 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 x^{2} y^{2}+x^{3} y^{3}}{16 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
12.837 |
|
| \begin{align*}
y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 x^{2} y^{2}+x^{3} y^{3}}{32 y x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.639 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x \left (x^{2}+y x +1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.247 |
|
| \begin{align*}
y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
4.604 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.161 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 x^{2} y^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
7.779 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.293 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 y x +4 x^{4}-3 x^{3}+y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.549 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 x^{2} y^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
7.792 |
|
| \begin{align*}
y^{\prime }&=\frac {x y \ln \left (x \right )+x^{2} \ln \left (x \right )-2 y x -x^{2}-y^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x \left (-y+x \ln \left (x \right )-x \right )} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.922 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.698 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{x^{2}-y^{2}-1}}}{-y^{2}-2 y x -x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{x^{2}-y^{2}-1}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
13.171 |
|
| \begin{align*}
y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.579 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 y a^{2} x^{4}+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.803 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}+96 a x y^{2}+12 x^{4} y+48 a \,x^{3} y+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
7.258 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+y x +x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.162 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 y a^{2} x^{4}}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 b^{2} x^{4} a}{16}+\frac {b^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.138 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} y^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 a \,x^{3} y}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.011 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sin \left (\frac {y}{x}\right ) y+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
35.214 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1446.041 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-y^{6} a^{2}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.996 |
|
| \begin{align*}
y^{\prime }&=-\frac {8 x \left (a -1\right ) \left (a +1\right )}{8+x^{6}+2 x^{4}-8 y+2 y^{4}-8 a^{2}-4 a^{2} x^{6}-y^{6} a^{2}-6 y^{4} a^{2} x^{2}-9 y^{2} a^{2} x^{4}+4 x^{2} y^{2}+y^{6}+4 a^{4} y^{2} x^{2}+3 x^{2} y^{4}-8 y^{2} a^{2} x^{2}+3 y^{2} x^{4}-2 y^{4} a^{2}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-6 a^{2} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-2 a^{6} x^{4}+6 a^{4} x^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.558 |
|
| \begin{align*}
y^{\prime }&=\frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-y \sin \left (\frac {y}{x}\right ) x -\sin \left (\frac {y}{x}\right ) y+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
41.267 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right )^{3}}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
10.782 |
|
| \begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
6.082 |
|
| \begin{align*}
y^{\prime }&=y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.025 |
|
| \begin{align*}
y^{\prime }&=y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.097 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
6.920 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2}+y x +x^{2}+x \right )}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.948 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
5.787 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.575 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right ) \left (x^{2} y^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.640 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+y x}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
4.439 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| \begin{align*}
y^{\prime }&=f \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.737 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{-n -2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.412 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
x^{4} y^{\prime }&=-y^{2} x^{4}-a^{2} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.360 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{n} y^{2}+b y+c \,x^{-n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.975 |
|
| \begin{align*}
\left (a x +c \right ) y^{\prime }&=\alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.631 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (1-a \right ) x^{2}-b&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.503 |
|
| \begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime }&=y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.358 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.657 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
35.550 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.902 |
|
| \begin{align*}
x y^{\prime }&=\left (a y+b \ln \left (x \right )\right )^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
31.234 |
|
| \begin{align*}
y y^{\prime }-y&=A x +B \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| \begin{align*}
y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
61.210 |
|
| \begin{align*}
y y^{\prime }&=\left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
43.762 |
|
| \begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+k x +b&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
95.445 |
|
| \begin{align*}
\left (y+a x +b \right ) y^{\prime }&=\alpha y+\beta x +\gamma \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
82.632 |
|
| \begin{align*}
\left (x^{2}+y x +a \right ) y^{\prime }&=y^{2}+y x +b \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.896 |
|
| \begin{align*}
\left (2 A x y+B \,x^{2}+b \right ) y^{\prime }&=A y^{2}+k \left (A k +B \right ) x^{2}+c \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
95.062 |
|
| \begin{align*}
\left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B x y-\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.636 |
|
| \begin{align*}
y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
16.392 |
|
| \begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\sqrt {a x +b}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
27.479 |
|
| \begin{align*}
y^{\prime }&=a x y^{3}+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
14.244 |
|
| \begin{align*}
y^{\prime }&=a \,x^{1+2 n} y^{3}+b \,x^{-n -2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
21.765 |
|
| \begin{align*}
x y^{\prime }&=3 x^{1+2 n} y^{3}+\left (b x -n \right ) y+c \,x^{1-n} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
12.214 |
|
| \begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
9.835 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
9.052 |
|
| \begin{align*}
\frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.938 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| \begin{align*}
6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.004 |
|
| \begin{align*}
\left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.024 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.432 |
|
| \begin{align*}
2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.731 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.502 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
77.725 |
|
| \begin{align*}
y^{3}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.206 |
|
| \begin{align*}
x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.524 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
41.441 |
|
| \begin{align*}
4 x -y+2+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.691 |
|
| \begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.238 |
|
| \begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.765 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.793 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.688 |
|
| \begin{align*}
y^{\prime }-\frac {y+1}{x +1}&=\sqrt {y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
12.006 |
|
| \begin{align*}
x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
185.912 |
|
| \begin{align*}
2 x^{3} y-y^{2}-\left (2 x^{4}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.605 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| \begin{align*}
\frac {x y^{\prime }-y}{\sqrt {x^{2}-y^{2}}}&=x y^{\prime } \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
14.428 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.590 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.736 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.553 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.086 |
|
| \begin{align*}
3 x^{2}+6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
36.036 |
|
| \begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.839 |
|
| \begin{align*}
x y^{\prime }-y+2 x^{2} y-x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.458 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.019 |
|
| \begin{align*}
x +y y^{\prime }+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.555 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
36.295 |
|
| \begin{align*}
y^{\prime }-x^{2} y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.277 |
|
| \begin{align*}
\left (-x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.411 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.279 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.194 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.450 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.528 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+3 y\right )-2 y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
42.439 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.521 |
|
| \begin{align*}
5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.957 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.417 |
|
| \begin{align*}
3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.939 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.404 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.540 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )+\sqrt {1+x^{2}+y^{2}}\, \left (-x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.235 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.237 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.599 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.996 |
|
| \begin{align*}
2 x y^{\prime }-y+\ln \left (y^{\prime }\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.415 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.775 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=a^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
135.917 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+y^{2}&=x^{2} y^{2}+x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
21.478 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.268 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.992 |
|
| \begin{align*}
x^{\prime }+2 x&=t^{2}+4 t +7 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| \begin{align*}
2 x^{\prime } t&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.815 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.390 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-t -1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.597 |
|
| \begin{align*}
R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.027 |
|
| \begin{align*}
\left (t +1\right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| \begin{align*}
x^{\prime }&=\left (4 t -x\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.445 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.350 |
|
| \begin{align*}
x^{\prime }&=t^{2} {\mathrm e}^{-x} \\
x \left (0\right ) &= \ln \left (2\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.116 |
|
| \begin{align*}
T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\
T \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.295 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.769 |
|
| \begin{align*}
x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.272 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.826 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y t}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.196 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{t}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.506 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
x^{\prime }+2 x t&={\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| \begin{align*}
x^{\prime } t&=-x+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.000 |
|
| \begin{align*}
x^{\prime }+\frac {5 x}{t}&=t +1 \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.203 |
|
| \begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.264 |
|
| \begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.405 |
|
| \begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.690 |
|
| \begin{align*}
x^{\prime }&=2 x t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.854 |
|
| \begin{align*}
x^{\prime }&=\left (t +x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.963 |
|
| \begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.874 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
68.100 |
|
| \begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.092 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.992 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.270 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.280 |
|
| \begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| \begin{align*}
y^{\prime }+y&=x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.906 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.989 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.360 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.443 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.292 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.574 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\
y \left (-1\right ) &= {\mathrm e}+3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.255 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x -2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.105 |
|
| \begin{align*}
3 x +2 y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.899 |
|
| \begin{align*}
\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
51.015 |
|
| \begin{align*}
\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}}&=0 \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
10.504 |
|
| \begin{align*}
\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}}&=0 \\
y \left (1\right ) &= 8 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✗ |
✗ |
28.430 |
|
| \begin{align*}
4 x +3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.530 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.958 |
|
| \begin{align*}
y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
5.866 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.103 |
|
| \begin{align*}
y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.437 |
|
| \begin{align*}
2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.433 |
|
| \begin{align*}
\tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.650 |
|
| \begin{align*}
x +y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.654 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.812 |
|
| \begin{align*}
v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.033 |
|
| \begin{align*}
x \tan \left (\frac {y}{x}\right )+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.479 |
|
| \begin{align*}
\left (2 s^{2}+2 t s+t^{2}\right ) s^{\prime }+s^{2}+2 t s-t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.707 |
|
| \begin{align*}
x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.282 |
|
| \begin{align*}
y+2+y \left (x +4\right ) y^{\prime }&=0 \\
y \left (-3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.194 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\
y \left (2\right ) &= 6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.297 |
|
| \begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.433 |
|
| \begin{align*}
3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.243 |
|
| \begin{align*}
x +2 y+\left (2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.228 |
|
| \begin{align*}
3 x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
41.424 |
|
| \begin{align*}
x^{2}+2 y^{2}+\left (4 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.094 |
|
| \begin{align*}
2 x^{2}+2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.360 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.851 |
|
| \begin{align*}
x^{4} y^{\prime }+2 x^{3} y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.833 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.289 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.124 |
|
| \begin{align*}
x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.630 |
|
| \begin{align*}
\left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.472 |
|
| \begin{align*}
x y^{\prime }+y x +y-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.945 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| \begin{align*}
x y^{\prime }+y&=-2 x^{6} y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.737 |
|
| \begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.638 |
|
| \begin{align*}
2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.355 |
|
| \begin{align*}
y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.752 |
|
| \begin{align*}
x y^{\prime }+y&=\left (y x \right )^{{3}/{2}} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
22.630 |
|
| \begin{align*}
a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.646 |
|
| \begin{align*}
y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| \begin{align*}
y^{\prime }&=-8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.453 |
|
| \begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.363 |
|
| \begin{align*}
\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
11.136 |
|
| \begin{align*}
y-1+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.804 |
|
| \begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.492 |
|
| \begin{align*}
3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.406 |
|
| \begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| \begin{align*}
2 x^{2}+y x +y^{2}+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
66.481 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
24.229 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&={\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.536 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.792 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.299 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+y^{2}}{2 y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.047 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.500 |
|
| \begin{align*}
8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
10.054 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.650 |
|
| \begin{align*}
4 x y y^{\prime }&=1+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.404 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
65.532 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.770 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
204.229 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
77.136 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.212 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.336 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.794 |
|
| \begin{align*}
10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
56.347 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.226 |
|
| \begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
88.581 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.925 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
50.408 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \begin{align*}
x^{\prime }&=t^{3} \left (1-x\right ) \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.209 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.720 |
|
| \begin{align*}
x^{\prime }&=x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.314 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.172 |
|
| \begin{align*}
x y^{\prime }&=k y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.968 |
|
| \begin{align*}
i^{\prime }&=p \left (t \right ) i \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.189 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.553 |
|
| \begin{align*}
x^{\prime }+x t&=4 t \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.193 |
|
| \begin{align*}
x^{\prime }+5 x&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.521 |
|
| \begin{align*}
y x +y^{2}+x^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.531 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
65.538 |
|
| \begin{align*}
12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
54.057 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.208 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.946 |
|
| \begin{align*}
-x y^{\prime }+y&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.279 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.672 |
|
| \begin{align*}
x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.999 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.130 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
39.815 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y^{3}+x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.829 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.363 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.685 |
|
| \begin{align*}
y^{\prime }&=\left (x -5 y\right )^{{1}/{3}}+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.173 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.768 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.574 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.174 |
|
| \begin{align*}
3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
34.110 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.015 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.722 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.608 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.650 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.506 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.098 |
|
| \begin{align*}
x^{2} y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.618 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.096 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.033 |
|
| \begin{align*}
5 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.583 |
|
| \begin{align*}
x y \left (1-{y^{\prime }}^{2}\right )&=\left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
158.413 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.102 |
|
| \begin{align*}
1+y-\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.510 |
|
| \begin{align*}
y-a +x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.507 |
|
| \begin{align*}
z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.939 |
|
| \begin{align*}
1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.344 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.925 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.155 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.822 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.894 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.452 |
|
| \begin{align*}
x +y+\left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.634 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.001 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.845 |
|
| \begin{align*}
2 \sqrt {t s}-s+t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.827 |
|
| \begin{align*}
t -s+t s^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.657 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.640 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right )&=y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.719 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
101.931 |
|
| \begin{align*}
x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.075 |
|
| \begin{align*}
x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.358 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
80.047 |
|
| \begin{align*}
\frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
127.216 |
|
| \begin{align*}
y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.545 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.015 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.966 |
|
| \begin{align*}
y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.880 |
|
| \begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.707 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.025 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.723 |
|
| \begin{align*}
x y^{\prime }&=\left (y \ln \left (x \right )-2\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.195 |
|
| \begin{align*}
\left (y^{3}-x \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
43.544 |
|
| \begin{align*}
\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.905 |
|
| \begin{align*}
\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.918 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.929 |
|
| \begin{align*}
y y^{\prime }+x&=\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
7.246 |
|
| \begin{align*}
y&=x y^{\prime }+y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.948 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.579 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.068 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-y x -\alpha &=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.287 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.157 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.304 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.314 |
|
| \begin{align*}
x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.606 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.713 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.433 |
|
| \begin{align*}
2 x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.534 |
|
| \begin{align*}
y^{\prime }-2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.058 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 x -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.802 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.382 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.199 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.401 |
|
| \begin{align*}
y^{\prime }&=-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.827 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.339 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.168 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.445 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.685 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.851 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.345 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.434 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.741 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.339 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.466 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.672 |
|
| \begin{align*}
y^{\prime }&=\left (y x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
41.475 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y-4}{x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.937 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
46.973 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (6\right ) &= -9 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
20.479 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.307 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
85.439 |
|
| \begin{align*}
y^{\prime }&=y x +x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.993 |
|
| \begin{align*}
x \,{\mathrm e}^{y}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.596 |
|
| \begin{align*}
y-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.286 |
|
| \begin{align*}
2 x y y^{\prime }+y^{2}&=-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.841 |
|
| \begin{align*}
y^{\prime }&=\frac {-y x +1}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.907 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.773 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{-y x +1} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
102.325 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -1}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.614 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.562 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.497 |
|
| \begin{align*}
x -y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.604 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.597 |
|
| \begin{align*}
x y \left (1-y\right )-2 y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.324 |
|
| \begin{align*}
\left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.840 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.630 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.243 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.570 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.170 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
16.067 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.271 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.366 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.710 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
43.302 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
32.628 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.229 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
89.987 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.071 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.029 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.540 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
21.301 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
11.782 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
16.325 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (1\right ) &= -{\frac {1}{5}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
4.345 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| \begin{align*}
y^{\prime }&=y^{2} t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.696 |
|
| \begin{align*}
y^{\prime }&=t^{4} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.281 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.460 |
|
| \begin{align*}
v^{\prime }&=t^{2} v-2-2 v+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.952 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y t +t +y+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.822 |
|
| \begin{align*}
w^{\prime }&=\frac {w}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.826 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.709 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.678 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.564 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
3.787 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=t +y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=2 y-t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.912 |
|
| \begin{align*}
y^{\prime }&=y t +t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| \begin{align*}
y^{\prime }&=t +y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (1+y\right ) \left (t -2\right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.416 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{-2+y} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.595 |
|
| \begin{align*}
y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.600 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 10 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
-2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }+2 y&=3 t^{2}+2 t -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.441 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.832 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{t}+t^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.984 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.272 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.934 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
y^{\prime }&=y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{7 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{t^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
y^{\prime }&=t +\frac {2 y}{t +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| \begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| \begin{align*}
y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3}+y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\prime }&=2 y t +3 t \,{\mathrm e}^{t^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+1+y+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.130 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| \begin{align*}
y y^{\prime }&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.122 |
|
| \begin{align*}
y^{\prime }+3 y x&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.857 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }&=y+3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| \begin{align*}
\left (-2+y\right ) y^{\prime }&=x -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.656 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.627 |
|
| \begin{align*}
y^{\prime }+y x&=4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.221 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.156 |
|
| \begin{align*}
x y y^{\prime }&=y^{2}+9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.000 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.335 |
|
| \begin{align*}
y^{\prime }&=2 x -1+2 y x -y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.853 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.159 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.648 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.703 |
|
| \begin{align*}
\left (y^{2}-1\right ) y^{\prime }&=4 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.142 |
|
| \begin{align*}
y^{\prime }&=3 x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.119 |
|
| \begin{align*}
y^{\prime }-3 x^{2} y^{2}&=-3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.412 |
|
| \begin{align*}
y^{\prime }-3 x^{2} y^{2}&=3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
5.263 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-1}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.401 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.194 |
|
| \begin{align*}
2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime }&=4 y+16 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.818 |
|
| \begin{align*}
x y^{\prime }+3 y-10 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.859 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.569 |
|
| \begin{align*}
x y^{\prime }+\left (2+5 x \right ) y&=\frac {20}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| \begin{align*}
x y^{\prime }+3 y&=20 x^{2} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.948 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2} \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3+3 x^{2}-y\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.776 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} {\mathrm e}^{-x^{2}} \\
y \left (3\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.556 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.673 |
|
| \begin{align*}
\cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.137 |
|
| \begin{align*}
y^{\prime }&=1+\left (-x +y\right )^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.974 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.340 |
|
| \begin{align*}
\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )&=1+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.405 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.777 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.657 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.469 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.084 |
|
| \begin{align*}
3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.889 |
|
| \begin{align*}
y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.254 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.941 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.358 |
|
| \begin{align*}
\left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
59.980 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3}-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.582 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.368 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.310 |
|
| \begin{align*}
y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.896 |
|
| \begin{align*}
y^{\prime }+2 x&=2 \sqrt {x^{2}+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
7.375 |
|
| \begin{align*}
y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.122 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.864 |
|
| \begin{align*}
2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.250 |
|
| \begin{align*}
2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.744 |
|
| \begin{align*}
2-2 x +3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.331 |
|
| \begin{align*}
4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
130.420 |
|
| \begin{align*}
1+\ln \left (y x \right )+\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
6.089 |
|
| \begin{align*}
1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.569 |
|
| \begin{align*}
{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \begin{align*}
1+y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.201 |
|
| \begin{align*}
y+\left (y^{4}-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
30.619 |
|
| \begin{align*}
\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
79.165 |
|
| \begin{align*}
3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.189 |
|
| \begin{align*}
2 x \left (y+1\right )-y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.193 |
|
| \begin{align*}
6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.815 |
|
| \begin{align*}
x y^{\prime }&=2 y-6 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.139 |
|
| \begin{align*}
x y^{\prime }&=2 y^{2}-6 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.275 |
|
| \begin{align*}
4 y^{2}-x^{2} y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.467 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=\sqrt {x^{2} y^{2}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.374 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.584 |
|
| \begin{align*}
4 y x -6+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| \begin{align*}
x y^{2}-6+x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \begin{align*}
x^{3}+y^{3}+x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.812 |
|
| \begin{align*}
3 y-x^{3}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.718 |
|
| \begin{align*}
3 x y^{3}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.349 |
|
| \begin{align*}
2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.788 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x -3 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.390 |
|
| \begin{align*}
\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.413 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.858 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.744 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.201 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.954 |
|
| \begin{align*}
y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.528 |
|
| \begin{align*}
1-\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.242 |
|
| \begin{align*}
y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.738 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \begin{align*}
2 y-6 x +\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| \begin{align*}
\left (3-x +y\right )^{2} \left (y^{\prime }-1\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \begin{align*}
y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.927 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.627 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| \begin{align*}
y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.948 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| \begin{align*}
2 x -y-y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.425 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.482 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.132 |
|
| \begin{align*}
3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.858 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.155 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.125 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.597 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.208 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.573 |
|
| \begin{align*}
t y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| \begin{align*}
t y^{\prime }+y&=t^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.173 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.471 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
41.807 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.146 |
|
| \begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.724 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{2 t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.402 |
|
| \begin{align*}
\frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.062 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 y+10 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 y+2 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
y^{\prime }&=\frac {5^{-t}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
y^{\prime }&=y^{2} t^{2}+y^{2}-t^{2}-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.022 |
|
| \begin{align*}
4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.948 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {t}}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.276 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y}{t}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.931 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.411 |
|
| \begin{align*}
y^{\prime }&=\frac {y+3}{1+3 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.913 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.405 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y+1}{x +3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.253 |
|
| \begin{align*}
y^{\prime }&=\cos \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.866 |
|
| \begin{align*}
y^{\prime }&=y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.796 |
|
| \begin{align*}
y^{\prime }&=-\frac {-2+y}{x -2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.931 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.388 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{2 x -2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.173 |
|
| \begin{align*}
y^{\prime }&=\left (x +y-4\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.647 |
|
| \begin{align*}
y^{\prime }&=y f \left (t \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.602 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \begin{align*}
-y+y^{\prime }&=t^{2}-2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| \begin{align*}
t y^{\prime }+y&=t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.981 |
|
| \begin{align*}
t y^{\prime }+y&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.460 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| \begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.884 |
|
| \begin{align*}
y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.337 |
|
| \begin{align*}
y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.444 |
|
| \begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.191 |
|
| \begin{align*}
y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.408 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.590 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.261 |
|
| \begin{align*}
y^{\prime }-x&=y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \begin{align*}
y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.802 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| \begin{align*}
p^{\prime }&=t^{3}+\frac {p}{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.092 |
|
| \begin{align*}
v^{\prime }+v&={\mathrm e}^{-s} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| \begin{align*}
-y+y^{\prime }&=4 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.262 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.431 |
|
| \begin{align*}
2 y t +y^{\prime }&=2 t \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.877 |
|
| \begin{align*}
\left (t^{2}+4\right ) y^{\prime }+2 y t&=2 t \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.168 |
|
| \begin{align*}
x^{\prime }&=x+t +1 \\
x \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
y+y^{\prime }&=2-{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }-5 y&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.085 |
|
| \begin{align*}
3 y+y^{\prime }&=27 t^{2}+9 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| \begin{align*}
y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }-3 y&=27 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.116 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.923 |
|
| \begin{align*}
y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.145 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| \begin{align*}
\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.264 |
|
| \begin{align*}
\ln \left (y t \right )+\frac {t y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
10.802 |
|
| \begin{align*}
{\mathrm e}^{y t}+\frac {t \,{\mathrm e}^{y t} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.341 |
|
| \begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.079 |
|
| \begin{align*}
-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
21.697 |
|
| \begin{align*}
2 y t +\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.218 |
|
| \begin{align*}
2 t y^{3}+\left (1+3 y^{2} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.584 |
|
| \begin{align*}
\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.070 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.535 |
|
| \begin{align*}
\left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
9.089 |
|
| \begin{align*}
-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.994 |
|
| \begin{align*}
2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.539 |
|
| \begin{align*}
1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.077 |
|
| \begin{align*}
1+5 t -y-\left (t +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.158 |
|
| \begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.017 |
|
| \begin{align*}
y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.483 |
|
| \begin{align*}
2 y t +y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.727 |
|
| \begin{align*}
5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.412 |
|
| \begin{align*}
\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
70.855 |
|
| \begin{align*}
2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
50.546 |
|
| \begin{align*}
y+y^{\prime }&=t y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.033 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.779 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.812 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.812 |
|
| \begin{align*}
\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.664 |
|
| \begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.856 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.784 |
|
| \begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.533 |
|
| \begin{align*}
2 y-3 t +t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.910 |
|
| \begin{align*}
y t -y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.751 |
|
| \begin{align*}
t^{2}+y t +y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
35.491 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.119 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.000 |
|
| \begin{align*}
t -y+t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| \begin{align*}
y+\left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.817 |
|
| \begin{align*}
2 t^{2}-7 y t +5 y^{2}+t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
77.904 |
|
| \begin{align*}
y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.272 |
|
| \begin{align*}
y^{2}&=\left (y t -4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.619 |
|
| \begin{align*}
y-\left (3 \sqrt {y t}+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.286 |
|
| \begin{align*}
t y y^{\prime }-{\mathrm e}^{-\frac {y}{t}} t^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.504 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.944 |
|
| \begin{align*}
t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.511 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 y t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.437 |
|
| \begin{align*}
t +y-t y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.550 |
|
| \begin{align*}
t y^{\prime }-y-\sqrt {t^{2}+y^{2}}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.143 |
|
| \begin{align*}
t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.006 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.387 |
|
| \begin{align*}
t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.141 |
|
| \begin{align*}
y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
23.554 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.165 |
|
| \begin{align*}
5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.999 |
|
| \begin{align*}
3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| \begin{align*}
2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.522 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.453 |
|
| \begin{align*}
1+y-t y^{\prime }&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
6.999 |
|
| \begin{align*}
y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.891 |
|
| \begin{align*}
t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.707 |
|
| \begin{align*}
y^{\prime }&=\frac {-t^{2}+y^{2}}{y t} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.763 |
|
| \begin{align*}
y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.125 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.450 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.041 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.225 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.687 |
|
| \begin{align*}
3 t +\left (t -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.168 |
|
| \begin{align*}
y-t +\left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.254 |
|
| \begin{align*}
y-x +y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \begin{align*}
y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
93.879 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.959 |
|
| \begin{align*}
x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.369 |
|
| \begin{align*}
y t +y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.513 |
|
| \begin{align*}
x^{\prime }+\frac {x}{y}&=y^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.079 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.957 |
|
| \begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| \begin{align*}
y-t y^{\prime }&=2 y^{2} \ln \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.825 |
|
| \begin{align*}
2 x -y-2+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.851 |
|
| \begin{align*}
\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.620 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
9.928 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t -2} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \begin{align*}
y^{\prime }-4 y&=t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y^{\prime }+4 y&=t \,{\mathrm e}^{-4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.636 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.878 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.735 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.424 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.931 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.688 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.720 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.140 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.277 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.415 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.790 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
x y^{\prime }&=2 x -y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.273 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.685 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.597 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.650 |
|
| \begin{align*}
1+y^{2}&=x y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.719 |
|
| \begin{align*}
\ln \left (y\right ) y+x y^{\prime }&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
7.334 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.635 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.227 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.668 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.116 |
|
| \begin{align*}
a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\
y \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
13.954 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.576 |
|
| \begin{align*}
x^{3} y^{\prime }-\sin \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
7.881 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\
y \left (-\infty \right ) &= \frac {7 \pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
7.266 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.640 |
|
| \begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.585 |
|
| \begin{align*}
x y^{\prime }&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.022 |
|
| \begin{align*}
x -y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
x y^{\prime }&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.852 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.401 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.330 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.005 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.046 |
|
| \begin{align*}
x +y-2+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.144 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
82.389 |
|
| \begin{align*}
x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.595 |
|
| \begin{align*}
x +y+\left (x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.181 |
|
| \begin{align*}
2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.321 |
|
| \begin{align*}
8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.606 |
|
| \begin{align*}
x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.153 |
|
| \begin{align*}
x +y+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.145 |
|
| \begin{align*}
2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.775 |
|
| \begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.277 |
|
| \begin{align*}
y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
10.386 |
|
| \begin{align*}
x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
25.529 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| \begin{align*}
x^{2}-x y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.442 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.595 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.251 |
|
| \begin{align*}
\left (2 x -y^{2}\right ) y^{\prime }&=2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.676 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.760 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.793 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.554 |
|
| \begin{align*}
3 x y^{2} y^{\prime }-2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.244 |
|
| \begin{align*}
\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| \begin{align*}
y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.844 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.482 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.166 |
|
| \begin{align*}
\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
38.215 |
|
| \begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.286 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.351 |
|
| \begin{align*}
3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
27.628 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.608 |
|
| \begin{align*}
x -y x +\left (x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.956 |
|
| \begin{align*}
y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.536 |
|
| \begin{align*}
x y^{\prime }-y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.030 |
|
| \begin{align*}
x^{2} y^{\prime }&=1+y x +x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.815 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.484 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.708 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.392 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.829 |
|
| \begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
95.180 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.888 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.191 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.913 |
|
| \begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.727 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.073 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.543 |
|
| \begin{align*}
x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.971 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.221 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.851 |
|
| \begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
8.734 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.449 |
|
| \begin{align*}
2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.225 |
|
| \begin{align*}
x^{2} y^{n} y^{\prime }&=2 x y^{\prime }-y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
24.056 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.118 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.762 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.543 |
|
| \begin{align*}
\left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
194.849 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.020 |
|
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.182 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.050 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.591 |
|
| \begin{align*}
y^{\prime }+y^{3} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.986 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.249 |
|
| \begin{align*}
y^{\prime }&=4 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
27.494 |
|
| \begin{align*}
y^{\prime }&=x \left (y-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.852 |
|
| \begin{align*}
y^{\prime }&=\left (1-12 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{8}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.377 |
|
| \begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.894 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{\theta } \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.868 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.430 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.955 |
|
| \begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.095 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\
y \left (0\right ) &= -\sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
15.498 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.810 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| \begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
7.580 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
10.971 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
14.471 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.550 |
|
| \begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.766 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.319 |
|
| \begin{align*}
2 y t +y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.694 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.166 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
-y+t y^{\prime }&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.644 |
|
| \begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.680 |
|
| \begin{align*}
t y^{\prime }+4 y&=t^{2}-t +1 \\
y \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.578 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| \begin{align*}
-y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.565 |
|
| \begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.290 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.724 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| \begin{align*}
-\frac {3 y}{2}+y^{\prime }&=3 t +3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.788 |
|
| \begin{align*}
y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.636 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.141 |
|
| \begin{align*}
y+\left (-4+t \right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.140 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.038 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.836 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{2 t +5 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.542 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
17.981 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
21.904 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.780 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.116 |
|
| \begin{align*}
y^{\prime }&=y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.870 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.632 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.656 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
42.231 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.685 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
49.365 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.427 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.695 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.834 |
|
| \begin{align*}
3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.631 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.912 |
|
| \begin{align*}
\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.856 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }&=y \left (y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.375 |
|
| \begin{align*}
y+\sqrt {x^{2}-y^{2}}&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
69.402 |
|
| \begin{align*}
x y y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
32.530 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.452 |
|
| \begin{align*}
x y^{\prime }-4 \sqrt {y^{2}-x^{2}}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.076 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
127.954 |
|
| \begin{align*}
\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.769 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.776 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (5\right ) &= 8 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
83.207 |
|
| \begin{align*}
t y^{\prime }+y&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.494 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{t}&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t -y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.563 |
|
| \begin{align*}
3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.161 |
|
| \begin{align*}
\left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.157 |
|
| \begin{align*}
1&=\left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.189 |
|
| \begin{align*}
y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.176 |
|
| \begin{align*}
\frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.043 |
|
| \begin{align*}
\left (2-x \right ) y^{\prime }&=y+2 \left (2-x \right )^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.840 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.655 |
|
| \begin{align*}
4 x y y^{\prime }&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.504 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.232 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.089 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.046 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.034 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.053 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.352 |
|
| \begin{align*}
3 y-7 x +7&=\left (3 x -7 y-3\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
54.477 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.309 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.558 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.575 |
|
| \begin{align*}
x y^{\prime }-4 y&=x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| \begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.317 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.444 |
|
| \begin{align*}
y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.039 |
|
| \begin{align*}
\left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }&=\left (1+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
8.462 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
\left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.691 |
|
| \begin{align*}
\frac {y y^{\prime }+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {-x y^{\prime }+y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✗ |
6.342 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.301 |
|
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.230 |
|
| \begin{align*}
\left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.824 |
|
| \begin{align*}
a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.340 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+y^{2}&=x^{2} y^{2}+x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.759 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
141.269 |
|
| \begin{align*}
y&=\frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
216.297 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
7.143 |
|
| \begin{align*}
y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.770 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
135.368 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.875 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.793 |
|
| \begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {1-x^{2} y^{2}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
32.204 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.309 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.709 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.040 |
|
| \begin{align*}
\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.266 |
|
| \begin{align*}
x y y^{\prime }&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.989 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.980 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.894 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.000 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \begin{align*}
\ln \left (y\right ) y-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.288 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.791 |
|
| \begin{align*}
{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.444 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.664 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.105 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.412 |
|
| \begin{align*}
x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.448 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.634 |
|
| \begin{align*}
x y^{\prime }&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.095 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.402 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.889 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.430 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.919 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.999 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.858 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
223.433 |
|
| \begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.673 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.207 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
40.450 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
39.999 |
|
| \begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.332 |
|
| \begin{align*}
1&=\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \\
\end{align*} |
[_exact, _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.398 |
|
| \begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.892 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
8.874 |
|
| \begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.023 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.442 |
|
| \begin{align*}
x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.707 |
|
| \begin{align*}
y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.792 |
|
| \begin{align*}
x +3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.341 |
|
| \begin{align*}
x y^{\prime }-y&=\left (1+y^{2}\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.028 |
|
| \begin{align*}
-x y^{\prime }+y&=x y^{3} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.131 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.554 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2}+9 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.886 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
857.964 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} y^{4} \left (x y^{\prime }+y\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.527 |
|
| \begin{align*}
x y^{\prime }+y+x^{2} y^{5} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.852 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.605 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
16.494 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.249 |
|
| \begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.437 |
|
| \begin{align*}
y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.973 |
|
| \begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.874 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.591 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| \begin{align*}
-x y^{\prime }+y&=y^{\prime } y^{2} {\mathrm e}^{y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.834 |
|
| \begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.780 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2} y+\ln \left (y\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.820 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.392 |
|
| \begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.967 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.434 |
|
| \begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
58.503 |
|
| \begin{align*}
x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.361 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.831 |
|
| \begin{align*}
x y y^{\prime }&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.481 |
|
| \begin{align*}
x^{2}+y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| \begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
\cos \left (x +y\right )&=x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
5.347 |
|
| \begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
22.507 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
98.308 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.951 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
115.187 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+2}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.552 |
|
| \begin{align*}
3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.724 |
|
| \begin{align*}
\frac {-x +y}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.189 |
|
| \begin{align*}
x y^{2}+y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x -2 y-1}{2 x +3 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.418 |
|
| \begin{align*}
3 y x +y^{2}+\left (3 y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.699 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.813 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.876 |
|
| \begin{align*}
x y^{\prime }+y x +y-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.697 |
|
| \begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.307 |
|
| \begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.649 |
|
| \begin{align*}
\left (t^{2}-x^{2}\right ) x^{\prime }&=x t \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.867 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.706 |
|
| \begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
x^{\prime }+x \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \begin{align*}
t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.023 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.345 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.443 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
69.461 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
78.055 |
|
| \begin{align*}
2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
69.056 |
|
| \begin{align*}
y y^{\prime }+x&=m y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
28.292 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.498 |
|
| \begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \begin{align*}
\left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.183 |
|
| \begin{align*}
\sqrt {t^{2}+T}&=T^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
11.440 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
y^{\prime }&=x \left (a y^{2}+b \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.588 |
|
| \begin{align*}
n^{\prime }&=\left (n^{2}+1\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 v \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.787 |
|
| \begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
v^{\prime }+2 u v&=2 u \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.285 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.280 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.441 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| \begin{align*}
x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.131 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
23.999 |
|
| \begin{align*}
5 x y y^{\prime }-x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.125 |
|
| \begin{align*}
\left (x^{2}+3 y x -y^{2}\right ) y^{\prime }-3 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.998 |
|
| \begin{align*}
\left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
23.458 |
|
| \begin{align*}
3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| \begin{align*}
\left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.715 |
|
| \begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
82.740 |
|
| \begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.193 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
56.342 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.398 |
|
| \begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.398 |
|
| \begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }&=x -y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.405 |
|
| \begin{align*}
\left (6 x -4 y+1\right ) y^{\prime }&=3 x -2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.010 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }-y-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.862 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.586 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.672 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.357 |
|
| \begin{align*}
\left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.677 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
74.422 |
|
| \begin{align*}
\left (y-3 x +3\right ) y^{\prime }&=2 y-x -4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
84.217 |
|
| \begin{align*}
x^{2}-4 y x -2 y^{2}+\left (y^{2}-4 y x -2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.678 |
|
| \begin{align*}
x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.905 |
|
| \begin{align*}
2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
69.279 |
|
| \begin{align*}
y-x y^{\prime }+\ln \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| \begin{align*}
\left (y x +1\right ) y-x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
52.365 |
|
| \begin{align*}
a \left (x y^{\prime }+2 y\right )&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.839 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.250 |
|
| \begin{align*}
x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.734 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.616 |
|
| \begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.958 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.306 |
|
| \begin{align*}
2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
16.763 |
|
| \begin{align*}
y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
49.539 |
|
| \begin{align*}
x y^{\prime }-a y&=x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.392 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.259 |
|
| \begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.968 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=3 x^{2} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.689 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.718 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.821 |
|
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.108 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.418 |
|
| \begin{align*}
2 x -y+1+\left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.220 |
|
| \begin{align*}
x y^{\prime }+\frac {y^{2}}{x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.112 |
|
| \begin{align*}
y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.125 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.259 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.426 |
|
| \begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
17.426 |
|
| \begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.958 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.359 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.536 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.748 |
|
| \begin{align*}
3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.342 |
|
| \begin{align*}
2 x^{2} y^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.201 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.362 |
|
| \begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.123 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \begin{align*}
x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.485 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
60.777 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.427 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.246 |
|
| \begin{align*}
\left (y x +1\right ) y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.783 |
|
| \begin{align*}
x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.227 |
|
| \begin{align*}
x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.372 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.079 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.457 |
|
| \begin{align*}
x y^{\prime }-y-\cos \left (\frac {1}{x}\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.747 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.660 |
|
| \begin{align*}
2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.696 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.983 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| \begin{align*}
\left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.372 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.934 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y-\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.485 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.635 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.603 |
|
| \begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }-x +y-3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.421 |
|
| \begin{align*}
x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.309 |
|
| \begin{align*}
y^{2}&=\left (y x -x^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.349 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.981 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.483 |
|
| \begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.786 |
|
| \begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
65.970 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }+7 y-5 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.992 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.832 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.245 |
|
| \begin{align*}
\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.524 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.559 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 x -y}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.276 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.910 |
|
| \begin{align*}
x -y-2-\left (2 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.457 |
|
| \begin{align*}
y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.824 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.238 |
|
| \begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.077 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.493 |
|
| \begin{align*}
y y^{\prime }+x&=\frac {a^{2} \left (x y^{\prime }-y\right )}{x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
5.040 |
|
| \begin{align*}
x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.260 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.232 |
|
| \begin{align*}
y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
34.628 |
|
| \begin{align*}
2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
70.983 |
|
| \begin{align*}
\frac {y y^{\prime }+x}{x y^{\prime }-y}&=\sqrt {\frac {a^{2}-x^{2}-y^{2}}{x^{2}+y^{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
110.355 |
|
| \begin{align*}
\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.732 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.488 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.637 |
|
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.521 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.541 |
|
| \begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.182 |
|
| \begin{align*}
2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.772 |
|
| \begin{align*}
\left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.525 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right )+\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.549 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.383 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.824 |
|
| \begin{align*}
y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
72.490 |
|
| \begin{align*}
y&=3 x +a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
y&=x +a \arctan \left (y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.810 |
|
| \begin{align*}
x&=y+a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.855 |
|
| \begin{align*}
-x y^{\prime }+y&=y y^{\prime }+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.508 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y&=\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.902 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
75.246 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
153.132 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
108.727 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
162.364 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.903 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
3.669 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.743 |
|
| \begin{align*}
1+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.916 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
91.812 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
49.796 |
|
| \begin{align*}
2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.701 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.834 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
16.408 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.792 |
|
| \begin{align*}
x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 x y y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.946 |
|
| \begin{align*}
x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.948 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.166 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.740 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.790 |
|
| \begin{align*}
x y^{\prime }&=y \left (-2 y+1\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.117 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.163 |
|
| \begin{align*}
s^{\prime }+2 s&=s t^{2} \\
s \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.470 |
|
| \begin{align*}
x^{\prime }-2 x&={\mathrm e}^{2 t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{3} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.777 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.487 |
|
| \begin{align*}
\sin \left (y x \right )+x y \cos \left (y x \right )+x^{2} \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.760 |
|
| \begin{align*}
y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.706 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.329 |
|
| \begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
x y^{\prime }-y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.092 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.146 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
21.276 |
|
| \begin{align*}
y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.447 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x +2}-{\mathrm e}^{\frac {y+1}{x +2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.811 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x +2}+{\mathrm e}^{\frac {y+1}{x +2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.133 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2}-{\mathrm e}^{\frac {x +y+1}{x +2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.829 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+1}{2 x +2+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.201 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y+1}{x +2 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
121.046 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.855 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.252 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y \left (-1+y\right )}{x \left (2-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.250 |
|
| \begin{align*}
y&=x y^{\prime }-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.271 |
|
| \begin{align*}
y^{\prime }-y+y^{2} {\mathrm e}^{x}+5 \,{\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= \eta \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.569 |
|
| \begin{align*}
\left (y x +1\right ) y&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.911 |
|
| \begin{align*}
y&=x y^{\prime }+a y^{\prime }+b \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
x^{\prime }-2 x \cos \left (t \right )&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.665 |
|
| \begin{align*}
x^{\prime }+\frac {x}{t^{2}-1}&=0 \\
x \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.472 |
|
| \begin{align*}
x^{\prime } t +x&=2 t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
t^{2} x^{\prime }-2 x t&=t^{5} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.832 |
|
| \begin{align*}
x^{\prime }&=2 x t \\
x \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.064 |
|
| \begin{align*}
x^{\prime }&=-x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.046 |
|
| \begin{align*}
x^{\prime }+a x&=b t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
x^{\prime }&=x+2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
x^{\prime }-2 x&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.927 |
|
| \begin{align*}
x^{\prime }+3 x&=-2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
x^{\prime }+a x&=b t \\
x \left (t_{0} \right ) &= x_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
x^{\prime }-x&=\frac {t}{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
x^{\prime }-2 x&=2 t \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t^{2}+1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.264 |
|
| \begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
x^{\prime }+x&=a t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \begin{align*}
x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.748 |
|
| \begin{align*}
x^{\prime }&=x t -t^{3} \\
x \left (a \right ) &= a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.918 |
|
| \begin{align*}
x^{\prime }&=x t -t^{3} \\
x \left (0\right ) &= a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.135 |
|
| \begin{align*}
x^{\prime }&=-t x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.230 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t} \left (x^{2}+1\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.875 |
|
| \begin{align*}
x^{\prime }&=\frac {t}{x} \\
x \left (\sqrt {2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.966 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{4 x^{3}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.780 |
|
| \begin{align*}
x^{\prime }&=-t^{2} x^{2} \\
x \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.530 |
|
| \begin{align*}
x^{\prime }&=5 t \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.065 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.529 |
|
| \begin{align*}
x^{\prime }&=2 t \sqrt {x} \\
x \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.448 |
|
| \begin{align*}
x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.784 |
|
| \begin{align*}
x +3 y+\left (3 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.770 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.436 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.418 |
|
| \begin{align*}
x -2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.950 |
|
| \begin{align*}
x +y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.743 |
|
| \begin{align*}
x +2 y+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.589 |
|
| \begin{align*}
x^{\prime }&=\frac {x+2 t}{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \begin{align*}
x^{\prime }&=\frac {t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.208 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.326 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.088 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t +1}{x-t +2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.062 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.944 |
|
| \begin{align*}
x^{\prime }&=-\frac {x+t +1}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.634 |
|
| \begin{align*}
x^{\prime }-x&=t x^{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.310 |
|
| \begin{align*}
x^{\prime }+2 x t&=-4 t x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.328 |
|
| \begin{align*}
x&=x^{\prime } t -{\mathrm e}^{x^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
5.090 |
|
| \begin{align*}
x&=x^{\prime } t -\ln \left (x^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
7.182 |
|
| \begin{align*}
x&=t \left (1+x^{\prime }\right )+x^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.565 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.042 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.542 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.774 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.783 |
|
| \begin{align*}
-2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.606 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (0\right ) &= a_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
11.514 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.405 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.319 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.948 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.922 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.442 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.323 |
|
| \begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.910 |
|
| \begin{align*}
2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.711 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
47.916 |
|
| \begin{align*}
x +2 y-4-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
42.184 |
|
| \begin{align*}
x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.718 |
|
| \begin{align*}
{\mathrm e}^{-y} \left (y^{\prime }+1\right )&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.515 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.988 |
|
| \begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
64.798 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.475 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
66.776 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
60.649 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.553 |
|
| \begin{align*}
y+x y^{\prime }+\frac {y^{3} \left (-x y^{\prime }+y\right )}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
19.236 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.128 |
|
| \begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.447 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
8.652 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+3 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.211 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {2 x}{y}}}{y^{2}+y^{2} {\mathrm e}^{\frac {2 x}{y}}+2 x^{2} {\mathrm e}^{\frac {2 x}{y}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.387 |
|
| \begin{align*}
y^{2}-x^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.719 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.529 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
105.995 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.870 |
|
| \begin{align*}
2 x y y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.270 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.587 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
99.834 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.792 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.643 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.872 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.758 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.957 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
17.003 |
|
| \begin{align*}
y-x y^{2}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.128 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.225 |
|
| \begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
2 y-8 x^{2}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.802 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.599 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
28.189 |
|
| \begin{align*}
3 x^{2} y+\left (y^{4}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.838 |
|
| \begin{align*}
y+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.766 |
|
| \begin{align*}
\left (x^{3}-y\right ) y-x \left (y+x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.671 |
|
| \begin{align*}
\frac {y^{2}-y x}{x y^{2}}+\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.280 |
|
| \begin{align*}
\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.436 |
|
| \begin{align*}
y^{\prime } \left (x +\frac {x^{2}}{y}\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
79.336 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.365 |
|
| \begin{align*}
y^{\prime }+q \left (x \right ) y&=0 \\
y \left (\textit {x\_0} \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.694 |
|
| \begin{align*}
2 y-1+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.070 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.159 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| \begin{align*}
y^{\prime }+y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.792 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| \begin{align*}
y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.033 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}+2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| \begin{align*}
y^{2}+\left (3 y x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
95.566 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y^{2}+2 y}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.755 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
70.533 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.414 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.125 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.454 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.438 |
|
| \begin{align*}
y^{\prime }&=-x^{2}-x -1-\left (2 x +1\right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.164 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
y^{\prime }-y&=3 x^{2}+x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.392 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.805 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.917 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
72.520 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.352 |
|
| \begin{align*}
x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.842 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.455 |
|
| \begin{align*}
2 x +y-3+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.066 |
|
| \begin{align*}
x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
49.704 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{2}+y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.024 |
|
| \begin{align*}
2 x^{4} y y^{\prime }+y^{4}&=4 x^{6} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
22.745 |
|
| \begin{align*}
x y^{\prime }&=x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.105 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.487 |
|
| \begin{align*}
y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.429 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.782 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.915 |
|
| \begin{align*}
3 x^{2}-2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.895 |
|
| \begin{align*}
1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.018 |
|
| \begin{align*}
r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.407 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.566 |
|
| \begin{align*}
r^{\prime }&=r \tan \left (t \right ) \\
r \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| \begin{align*}
y&=x y^{\prime }-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.950 |
|
| \begin{align*}
x^{3}-y^{3}+x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.930 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.531 |
|
| \begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.231 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
155.518 |
|
| \begin{align*}
x^{2}+2 y x -2 y^{2}+\left (y^{2}+2 y x -2 x^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.008 |
|
| \begin{align*}
a x -b y+\left (b x -a y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
28.576 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+\left (b \,x^{2}+2 c x y+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
100.565 |
|
| \begin{align*}
4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.582 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
30.010 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{2} y&=x^{5} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.023 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (x y^{\prime }+y\right )&=x y \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.937 |
|
| \begin{align*}
3 y+2 x y^{\prime }+4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
81.384 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.318 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
20.820 |
|
| \begin{align*}
y&=\left (2 x^{2} y^{3}-x \right ) y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✗ |
✗ |
✗ |
27.248 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| \begin{align*}
2-x -y+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.860 |
|
| \begin{align*}
2+3 x -5 y+7 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.650 |
|
| \begin{align*}
x -y-3+\left (3 x -3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.401 |
|
| \begin{align*}
2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.687 |
|
| \begin{align*}
x y \left (x y^{\prime }+y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.104 |
|
| \begin{align*}
\left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.015 |
|
| \begin{align*}
x y^{\prime }-y&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.526 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.785 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} x^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.526 |
|
| \begin{align*}
3 x^{2}+2 y x -2 y^{2}+\left (2 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.754 |
|
| \begin{align*}
2 x -y+1+\left (x -2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
129.203 |
|
| \begin{align*}
3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.410 |
|
| \begin{align*}
y&=x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
7.355 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.662 |
|
| \begin{align*}
x y^{2}&=-x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.069 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.209 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.119 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {y}{x}}}{x^{2}+y^{2} \sin \left (\frac {x}{y}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.874 |
|
| \begin{align*}
3 x^{2} y+\left (y+x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.576 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.181 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.689 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{x^{2} y+y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.697 |
|
| \begin{align*}
x -y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.061 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.472 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.832 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \begin{align*}
\frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
x +\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.390 |
|
| \begin{align*}
x^{2}+1+\frac {y^{\prime }}{y}&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.925 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.167 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.064 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.774 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.579 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
116.869 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.734 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.142 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.612 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 x}{y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.525 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.925 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +\sqrt {y x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.560 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +\left (x y^{2}\right )^{{1}/{3}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
96.681 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}+3 x^{2} y^{2}+y^{4}}{x^{3} y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
122.089 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.772 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (2\right ) &= -5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.274 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.616 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.795 |
|
| \begin{align*}
y \sin \left (x \right )+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.178 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.888 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.576 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
31.456 |
|
| \begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.969 |
|
| \begin{align*}
y^{\prime }&=\frac {-y+x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y+1-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.685 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.601 |
|
| \begin{align*}
x^{2}+y+y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| \begin{align*}
y+x^{3} y^{3}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.543 |
|
| \begin{align*}
y+y^{2} x^{4}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.424 |
|
| \begin{align*}
3 x^{2} y-x^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.967 |
|
| \begin{align*}
1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.983 |
|
| \begin{align*}
3 x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.817 |
|
| \begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.912 |
|
| \begin{align*}
y+x^{3}+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.211 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.922 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.181 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.085 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.013 |
|
| \begin{align*}
y^{\prime }-7 y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
y^{\prime }-7 y&=14 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.733 |
|
| \begin{align*}
y^{\prime }+x^{2} y&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.388 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.503 |
|
| \begin{align*}
y^{\prime }+6 y x&=0 \\
y \left (\pi \right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.045 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.180 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.579 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.706 |
|
| \begin{align*}
y^{\prime }-2 y&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.350 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.093 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.790 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.469 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.373 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.229 |
|
| \begin{align*}
y^{\prime }&=x^{2}+5 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.076 |
|
| \begin{align*}
r^{\prime }&=\sqrt {r t} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
28.721 |
|
| \begin{align*}
2 x +y+\left (x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.756 |
|
| \begin{align*}
y^{\prime }+y&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.551 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.756 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{-x +y} \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.967 |
|
| \begin{align*}
y^{\prime }&=3 x +2 y \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{y-2 x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
67.833 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
103.142 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.764 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\sqrt {y x +1}-1\right )^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
24.460 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.495 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.937 |
|
| \begin{align*}
2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.045 |
|
| \begin{align*}
x y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.016 |
|
| \begin{align*}
2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.782 |
|
| \begin{align*}
y^{\prime }&=8 y x +3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.680 |
|
| \begin{align*}
y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.478 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y\right ) \left (y+3\right )}{\left (-2+y\right ) \left (x +3\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.217 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.757 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.932 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.042 |
|
| \begin{align*}
x y^{\prime }&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.427 |
|
| \begin{align*}
x^{2}-y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.269 |
|
| \begin{align*}
x +2+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.917 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
8.254 |
|
| \begin{align*}
x y^{\prime }&=y-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.693 |
|
| \begin{align*}
y&=\left (2 x +3 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
82.610 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.598 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.470 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.966 |
|
| \begin{align*}
x -4 y+\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.720 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
146.321 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.560 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.071 |
|
| \begin{align*}
y^{\prime }&=\sqrt {2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.613 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.838 |
|
| \begin{align*}
\left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
215.521 |
|
| \begin{align*}
2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.717 |
|
| \begin{align*}
2 x +2 y+1+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.679 |
|
| \begin{align*}
2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
102.507 |
|
| \begin{align*}
y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.090 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
29.094 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{5}+3 x^{2} y^{2}}{2 x^{3} y-2 y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
10.822 |
|
| \begin{align*}
2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.563 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -3 y-5\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
24.027 |
|
| \begin{align*}
\sqrt {x +y+1}\, y^{\prime }&=\sqrt {x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.534 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
107.552 |
|
| \begin{align*}
x y^{\prime }-y&=\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
11.243 |
|
| \begin{align*}
3 x +4 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.371 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.822 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.336 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
47.763 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{-x +2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
42.015 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.926 |
|
| \begin{align*}
y^{2}+2 x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.763 |
|
| \begin{align*}
y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
28.680 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.158 |
|
| \begin{align*}
\frac {y}{\left (x +y\right )^{2}}-1+\left (1-\frac {x}{\left (x +y\right )^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
15.090 |
|
| \begin{align*}
x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
222.692 |
|
| \begin{align*}
3 x +2 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.781 |
|
| \begin{align*}
2 x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.408 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y^{3}-3 x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
30.994 |
|
| \begin{align*}
i^{\prime }&=\frac {t -i t}{t^{2}+1} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.033 |
|
| \begin{align*}
y^{3}+2 y \,{\mathrm e}^{x}+\left ({\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.474 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.667 |
|
| \begin{align*}
2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
183.906 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.799 |
|
| \begin{align*}
x y^{\prime }+3 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
y^{2}+x y y^{\prime }&=\left (2 y^{2}+1\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.572 |
|
| \begin{align*}
i^{\prime }+3 i&={\mathrm e}^{-2 t} \\
i \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.990 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.938 |
|
| \begin{align*}
r^{\prime }&=t -\frac {r}{3 t} \\
r \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.527 |
|
| \begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.062 |
|
| \begin{align*}
y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
119.921 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2} y+\ln \left (y\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
12.086 |
|
| \begin{align*}
x y^{\prime }+3&=4 x \,{\mathrm e}^{-y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.836 |
|
| \begin{align*}
y+\left (2 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.575 |
|
| \begin{align*}
y+\left (y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
19.782 |
|
| \begin{align*}
y+x^{3}+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.264 |
|
| \begin{align*}
x^{3}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.098 |
|
| \begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
97.595 |
|
| \begin{align*}
x^{3}-x y^{2}+y+\left (y^{3}-x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
13.523 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.810 |
|
| \begin{align*}
3-y+2 x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.102 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.408 |
|
| \begin{align*}
y^{\prime }&=\left (2 x^{2}-y \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.148 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.278 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.457 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.917 |
|
| \begin{align*}
y^{\prime } \left (y^{2}+2 x \right )&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
16.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.430 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.194 |
|
| \begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.259 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.026 |
|
| \begin{align*}
x +2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.080 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.019 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.792 |
|
| \begin{align*}
3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.705 |
|
| \begin{align*}
\left (2 y^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.638 |
|
| \begin{align*}
x y^{\prime }-y&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.408 |
|
| \begin{align*}
s^{\prime }&=\sqrt {\frac {1-t}{1-s}} \\
s \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✗ |
✓ |
✓ |
37.996 |
|
| \begin{align*}
2 y+3 x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.392 |
|
| \begin{align*}
x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.542 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x -y\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.207 |
|
| \begin{align*}
i^{\prime }+i&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.741 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
57.296 |
|
| \begin{align*}
\left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.060 |
|
| \begin{align*}
y^{\prime }&=3 x +2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.957 |
|
| \begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
91.246 |
|
| \begin{align*}
u^{\prime }&=-a \left (u-100 t \right ) \\
u \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.536 |
|
| \begin{align*}
u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.099 |
|
| \begin{align*}
s^{\prime }&=\frac {1}{s+t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.892 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y+3\right )^{2}}{4 x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.984 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.204 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.041 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
18.254 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.946 |
|
| \begin{align*}
y^{\prime }&=2-\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.964 |
|
| \begin{align*}
\left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.954 |
|
| \begin{align*}
r^{\prime }&={\mathrm e}^{t}-3 r \\
r \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.569 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
65.322 |
|
| \begin{align*}
{\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.953 |
|
| \begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.955 |
|
| \begin{align*}
y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.723 |
|
| \begin{align*}
3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
67.201 |
|
| \begin{align*}
y^{\prime }&=1-\left (x -y\right )^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.848 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
69.458 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
11.714 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.992 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.961 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +3 y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.787 |
|
| \begin{align*}
x^{2} y^{3}+2 x y^{2}+y+\left (x^{3} y^{2}-2 x^{2} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✗ |
✓ |
17.974 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y}+x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
133.130 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
101.184 |
|
| \begin{align*}
y^{\prime }+y x&=x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.901 |
|
| \begin{align*}
x^{2} y+2 y^{4}+\left (x^{3}+3 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
27.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.496 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.440 |
|
| \begin{align*}
x y^{\prime }&=x^{2} y^{2}-y+1 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.556 |
|
| \begin{align*}
y y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.799 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| \begin{align*}
1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.913 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.656 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.932 |
|
| \begin{align*}
x y^{\prime }&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.425 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.758 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.985 |
|
| \begin{align*}
x y^{\prime }-1+y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.740 |
|
| \begin{align*}
-x y^{\prime }+y&=3 y^{2} y^{\prime } \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
52.197 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.663 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.299 |
|
| \begin{align*}
x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
49.997 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x y^{\prime }+1\right )&=5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.274 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.458 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.797 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.235 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.312 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+1}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.102 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.687 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+2}{x +1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.246 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.365 |
|
| \begin{align*}
y^{\prime }-2 y x&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.562 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.153 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=5 x \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.053 |
|
| \begin{align*}
y^{\prime }-\frac {6 y}{x}&=7 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.011 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{x}&={\mathrm e}^{x} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.290 |
|
| \begin{align*}
n^{\prime }&=k n-b t \\
n \left (0\right ) &= n_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.663 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{k x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.975 |
|
| \begin{align*}
v^{\prime }&=60 t -4 v \\
v \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
\frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.847 |
|
| \begin{align*}
\left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
\cot \left (\theta \right ) r^{\prime }&=r+b \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\
r \left (\frac {\pi }{2}\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.185 |
|
| \begin{align*}
r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.280 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.977 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.576 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.497 |
|
| \begin{align*}
x y^{\prime }-y&=1 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.414 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.110 |
|
| \begin{align*}
y^{\prime }&=x -y x -y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.427 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-x +a \right ) y}{d \,x^{2}+c x +b} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.235 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
x y^{\prime }+y&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.411 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.008 |
|
| \begin{align*}
x y^{\prime }+6 y&=1+3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
x y^{\prime }+y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.577 |
|
| \begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
y y^{\prime }-7 y&=6 x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.835 |
|
| \begin{align*}
y y^{\prime }+x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.324 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
x y^{\prime }-\frac {y}{\ln \left (x \right )}&=0 \\
y \left ({\mathrm e}\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.324 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.950 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\
y \left (-1\right ) &= 16 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.899 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.414 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.214 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.021 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.603 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.957 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+\left (x \,{\mathrm e}^{y x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.540 |
|
| \begin{align*}
3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.578 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.655 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.953 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.352 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.108 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| \begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.394 |
|
| \begin{align*}
y+\left (2 x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.947 |
|
| \begin{align*}
y-2 x -x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
96.533 |
|
| \begin{align*}
5 x -y+3 x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.467 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.560 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.425 |
|
| \begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.363 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}}-\frac {y}{x}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.624 |
|
| \begin{align*}
y x -\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.997 |
|
| \begin{align*}
x -y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.595 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.463 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.398 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.174 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.653 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.766 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +2 y}{y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.926 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.413 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {2}\, \sqrt {\frac {x +y}{x}}}{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
61.371 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.941 |
|
| \begin{align*}
y^{\prime }+\sqrt {y}&=3 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✗ |
✗ |
10.328 |
|
| \begin{align*}
7 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.894 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.411 |
|
| \begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.217 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }&=x +y+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.096 |
|
| \begin{align*}
2 x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.658 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.260 |
|
| \begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| \begin{align*}
y x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.263 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.287 |
|
| \begin{align*}
x y y^{\prime }+x^{6}-2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.008 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
y+x y^{2}-\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
117.840 |
|
| \begin{align*}
x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.363 |
|
| \begin{align*}
y x -\left (y^{4}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.240 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y}{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.710 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.710 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.430 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.479 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} {\mathrm e}^{\frac {y}{x}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.846 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y-y^{3}}{x^{3}-x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.356 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.565 |
|
| \begin{align*}
y^{\prime }&=1+\frac {3 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.134 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+2 y^{2}-3 y x}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
59.445 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.737 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.036 |
|
| \begin{align*}
2 x +2 y-3+\left (1-2 y+2 x \right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.089 |
|
| \begin{align*}
x^{4}-3 y+3 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.162 |
|
| \begin{align*}
y^{3}+2 x y^{3}+1+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| \begin{align*}
x y^{2}+\left (3-2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
36.662 |
|
| \begin{align*}
y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.483 |
|
| \begin{align*}
y^{\prime }+3 y&=x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.537 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.387 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.819 |
|
| \begin{align*}
y^{\prime }-4 y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.484 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.467 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.289 |
|
| \begin{align*}
x -y+1+\left (2 y-2 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.767 |
|
| \begin{align*}
\left (x +2 y+2\right ) y^{\prime }&=3 x -y-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.385 |
|
| \begin{align*}
1+\left (1-3 x +y\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.704 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.309 |
|
| \begin{align*}
x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.293 |
|
| \begin{align*}
x y y^{\prime }+2 x +\frac {y^{2}}{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.486 |
|
| \begin{align*}
2 x y^{2}+\left (1-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
35.100 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.414 |
|
| \begin{align*}
{\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.946 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.045 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2}-1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{2}&=x^{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.383 |
|
| \begin{align*}
y^{\prime }-5 y&=3 x^{3}+4 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.000 |
|
| \begin{align*}
2 y-3 x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.426 |
|
| \begin{align*}
m y-n x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.055 |
|
| \begin{align*}
y^{\prime }&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.175 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{p} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.441 |
|
| \begin{align*}
1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.968 |
|
| \begin{align*}
y x -\left (x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
\cos \left (y\right )&=x y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| \begin{align*}
y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| \begin{align*}
r^{\prime }&=-2 r t \\
r \left (0\right ) &= r_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\
y \left (\infty \right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.170 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.502 |
|
| \begin{align*}
y x -\left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.698 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.231 |
|
| \begin{align*}
x^{2}+2 y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.590 |
|
| \begin{align*}
\left (x -y\right ) \left (4 x +y\right )+x \left (5 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
97.486 |
|
| \begin{align*}
5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
60.165 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.602 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.846 |
|
| \begin{align*}
x \left (x^{2}+y^{2}\right )^{2} \left (-x y^{\prime }+y\right )+y^{6} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.188 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.015 |
|
| \begin{align*}
y x -\left (x +2 y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.774 |
|
| \begin{align*}
v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
72.504 |
|
| \begin{align*}
x \csc \left (\frac {y}{x}\right )-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.421 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.274 |
|
| \begin{align*}
x -\ln \left (y\right ) y+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.803 |
|
| \begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.667 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \left (x y^{\prime }-y\right ) {\mathrm e}^{\frac {x}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.258 |
|
| \begin{align*}
t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.031 |
|
| \begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.861 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.809 |
|
| \begin{align*}
y-\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.115 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.291 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.523 |
|
| \begin{align*}
y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.977 |
|
| \begin{align*}
y^{2}+\left (x^{2}+3 y x +4 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.284 |
|
| \begin{align*}
y x +2 \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
42.006 |
|
| \begin{align*}
y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.355 |
|
| \begin{align*}
y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
101.601 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.986 |
|
| \begin{align*}
16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
74.984 |
|
| \begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.652 |
|
| \begin{align*}
-2 y x +\left (3 x^{2}-2 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
86.477 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.576 |
|
| \begin{align*}
2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.689 |
|
| \begin{align*}
1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \begin{align*}
1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.515 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.621 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.927 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.599 |
|
| \begin{align*}
x y^{2}+y-x +x \left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.218 |
|
| \begin{align*}
\frac {1}{\left (-y x +1\right )^{2}}+\left (y^{2}+\frac {x^{2}}{\left (-y x +1\right )^{2}}\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 1 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
6.289 |
|
| \begin{align*}
y \left (1+2 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
y \left (y^{3}-x \right )+x \left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.261 |
|
| \begin{align*}
x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
s \left (2+s^{2} t \right )+2 t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.249 |
|
| \begin{align*}
y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.610 |
|
| \begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.860 |
|
| \begin{align*}
\left (x^{3}-y^{5}\right ) y-x \left (x^{3}+y^{5}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
10.044 |
|
| \begin{align*}
\left (-y^{2}+x^{2}+1\right ) y-x \left (x^{2}-y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.805 |
|
| \begin{align*}
x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
4.259 |
|
| \begin{align*}
x^{4} y^{\prime }&=-x^{3} y-\csc \left (y x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.692 |
|
| \begin{align*}
1+y \tan \left (y x \right )+x \tan \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.625 |
|
| \begin{align*}
y \left (x^{2} y^{2}-m \right )+x \left (x^{2} y^{2}+n \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.223 |
|
| \begin{align*}
y \left (x^{2}+y\right )+x \left (x^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.737 |
|
| \begin{align*}
y \left (2-3 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| \begin{align*}
y \left (y^{2}+2 x \right )+x \left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.813 |
|
| \begin{align*}
y+2 \left (y^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| \begin{align*}
2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.582 |
|
| \begin{align*}
x^{n} y^{n +1}+a y+\left (x^{n +1} y^{n}+b x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
24.211 |
|
| \begin{align*}
x^{4}+2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.891 |
|
| \begin{align*}
3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.735 |
|
| \begin{align*}
x^{\prime } t&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.068 |
|
| \begin{align*}
y^{\prime }&=x -3 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
\left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
y-2+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
133.786 |
|
| \begin{align*}
2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=-2 y x +x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
y^{\prime }-m y&=c \,{\mathrm e}^{m x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
2 x \left (y-x^{2}\right )+y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| \begin{align*}
1+y x -\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.717 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=2 x \left (\left (a^{2}+x^{2}\right )^{2}+3 y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.108 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x -n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.126 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| \begin{align*}
\left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.932 |
|
| \begin{align*}
y^{\prime }&=x^{3}-2 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| \begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
\left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\
s \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
59.910 |
|
| \begin{align*}
x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
55.164 |
|
| \begin{align*}
x y^{\prime }&=x^{2} y^{2}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.404 |
|
| \begin{align*}
y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.683 |
|
| \begin{align*}
\left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
405.438 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.700 |
|
| \begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x y^{\prime } \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
42.677 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.437 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.851 |
|
| \begin{align*}
x y \left (1-y^{\prime }\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.693 |
|
| \begin{align*}
a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.727 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.902 |
|
| \begin{align*}
y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
17.394 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
17.764 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
15.612 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.724 |
|
| \begin{align*}
y \left (y \,{\mathrm e}^{y x}+1\right )+\left (x y \,{\mathrm e}^{y x}+{\mathrm e}^{y x}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
11.549 |
|
| \begin{align*}
y^{2}-\left (y x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
58.904 |
|
| \begin{align*}
y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.545 |
|
| \begin{align*}
y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.968 |
|
| \begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.566 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y x -3 x^{2}+2 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.054 |
|
| \begin{align*}
y^{2}+y-\left (y^{2}+2 y x +x \right ) y^{\prime }&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
5.976 |
|
| \begin{align*}
y^{3}-x^{3}&=x y \left (y y^{\prime }+x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.602 |
|
| \begin{align*}
y \left (x^{2} y^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.198 |
|
| \begin{align*}
3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.679 |
|
| \begin{align*}
y^{\prime }&=\left (9 x +4 y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
20.426 |
|
| \begin{align*}
y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.374 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| \begin{align*}
y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
54.107 |
|
| \begin{align*}
x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.039 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
59.968 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.565 |
|
| \begin{align*}
y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y+x \left (3 y x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
71.441 |
|
| \begin{align*}
2 y+x \left (x^{2} \ln \left (y\right )-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.962 |
|
| \begin{align*}
k \,{\mathrm e}^{2 v}-u -2 \,{\mathrm e}^{2 v} \left ({\mathrm e}^{2 v}+k u \right ) v^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.274 |
|
| \begin{align*}
x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.698 |
|
| \begin{align*}
x y^{\prime }-y&=x^{k} y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.611 |
|
| \begin{align*}
x y^{\prime }-y&=x^{k} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.331 |
|
| \begin{align*}
x y^{\prime }-y&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.753 |
|
| \begin{align*}
12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.049 |
|
| \begin{align*}
y^{\prime }&=2 \left (3 x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
38.848 |
|
| \begin{align*}
2 x y y^{\prime }&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| \begin{align*}
y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.103 |
|
| \begin{align*}
2 y^{3}-x^{3}+3 x y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.915 |
|
| \begin{align*}
x^{2}+6 y^{2}-4 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.492 |
|
| \begin{align*}
y-2-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.196 |
|
| \begin{align*}
x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.165 |
|
| \begin{align*}
2 x -y+\left (-6+4 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
31.938 |
|
| \begin{align*}
x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
73.102 |
|
| \begin{align*}
2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.936 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.724 |
|
| \begin{align*}
x -y+2+3 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.940 |
|
| \begin{align*}
x +y-1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.022 |
|
| \begin{align*}
3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.316 |
|
| \begin{align*}
x -2+4 \left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.386 |
|
| \begin{align*}
x -3 y+2+3 \left (x +3 y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.068 |
|
| \begin{align*}
6 x -3 y+2-\left (2 x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.438 |
|
| \begin{align*}
9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.921 |
|
| \begin{align*}
x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.934 |
|
| \begin{align*}
x +2 y-1-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.858 |
|
| \begin{align*}
x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
58.352 |
|
| \begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.990 |
|
| \begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.863 |
|
| \begin{align*}
x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.323 |
|
| \begin{align*}
x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 7 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.892 |
|
| \begin{align*}
y^{2}+\left (3 y x +y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
14.204 |
|
| \begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
8.870 |
|
| \begin{align*}
y \left (8 x -9 y\right )+2 x \left (x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.421 |
|
| \begin{align*}
x +3 y-5-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.342 |
|
| \begin{align*}
x -2 y+3+2 \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.445 |
|
| \begin{align*}
2 x +y-4+\left (x -3 y+12\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.888 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| \begin{align*}
x^{3} y+\left (3 x^{4}-y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.551 |
|
| \begin{align*}
a_{1} x +k y+c_{1} +\left (k x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
85.750 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
37.600 |
|
| \begin{align*}
x y^{\prime }&=x^{3} y^{3}-2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.941 |
|
| \begin{align*}
5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.704 |
|
| \begin{align*}
3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.323 |
|
| \begin{align*}
y^{\prime }&=x -y+2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| \begin{align*}
x +y-2-\left (x -4 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.596 |
|
| \begin{align*}
4+\left (x -y+2\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.379 |
|
| \begin{align*}
2 x +4 y-1-\left (x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.254 |
|
| \begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.272 |
|
| \begin{align*}
\left (x -1\right ) y-\left (x^{2}-2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.277 |
|
| \begin{align*}
x -2 y-1-\left (x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.583 |
|
| \begin{align*}
2 x -3 y+1-\left (3 x +2 y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.533 |
|
| \begin{align*}
4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.094 |
|
| \begin{align*}
x +4 y+3-\left (2 x -y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.754 |
|
| \begin{align*}
3 x -3 y-2-\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.702 |
|
| \begin{align*}
x -6 y+2+2 \left (x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
33.193 |
|
| \begin{align*}
x^{4}-4 x^{2} y^{2}-y^{4}+4 x^{3} y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.888 |
|
| \begin{align*}
x -y-1-2 \left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.235 |
|
| \begin{align*}
x -3 y+3+\left (3 x +y+9\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.778 |
|
| \begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
913.014 |
|
| \begin{align*}
t y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.128 |
|
| \begin{align*}
y^{\prime }&=2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.427 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.821 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \begin{align*}
y^{\prime }&=-y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.025 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \begin{align*}
t^{2} y^{\prime }&=1-2 y t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.717 |
|
| \begin{align*}
t y^{\prime }&=y-2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| \begin{align*}
y^{\prime }&=t y^{2}-y^{2}+t -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.442 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 y t \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.181 |
|
| \begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.739 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.621 |
|
| \begin{align*}
1-y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.438 |
|
| \begin{align*}
y^{3} y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.586 |
|
| \begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.258 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.888 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
45.994 |
|
| \begin{align*}
y+1+\left (-1+y\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.473 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.184 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
2 y t +y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.499 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (y\right )}{t} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.899 |
|
| \begin{align*}
\frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.239 |
|
| \begin{align*}
y t -\left (t +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.262 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{t} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.843 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.323 |
|
| \begin{align*}
t y^{\prime }+m y&=t \ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.923 |
|
| \begin{align*}
t \left (t +1\right ) y^{\prime }&=y+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| \begin{align*}
z^{\prime }&=2 t \left (z-t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t +1}&=\left (t +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.565 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=\frac {t +1}{t} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.403 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.520 |
|
| \begin{align*}
t y^{\prime }+2 \ln \left (t \right ) y&=4 \ln \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
t y^{\prime }+3 y&=t^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.023 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t&=1 \\
y \left (2\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
t^{2} y^{\prime }&=y^{2}+y t +t^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.897 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -3 y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.551 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\
y \left (2\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
60.368 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y t}{t^{2}+y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
22.048 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
65.507 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{y t} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.294 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
55.099 |
|
| \begin{align*}
t^{2} y^{\prime }&=y t +y \sqrt {t^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.465 |
|
| \begin{align*}
y t +y^{\prime }&=t y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.927 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime }-y t&=5 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.315 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.937 |
|
| \begin{align*}
y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.039 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 t -2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| \begin{align*}
y^{\prime }&=\left (t -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.882 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.275 |
|
| \begin{align*}
y^{\prime }+y \ln \left (y\right )&=y t \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.775 |
|
| \begin{align*}
y-t +\left (t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.851 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.092 |
|
| \begin{align*}
3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.379 |
|
| \begin{align*}
2 y t +2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.161 |
|
| \begin{align*}
t^{2}-y-t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.399 |
|
| \begin{align*}
\left (y^{3}-t \right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
27.822 |
|
| \begin{align*}
a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
44.018 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.570 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
62.964 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.885 |
|
| \begin{align*}
y^{\prime }&=t -y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| \begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.761 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
60.576 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.089 |
|
| \begin{align*}
y^{\prime }&=\cos \left (t +y\right ) \\
y \left (t_{0} \right ) &= y_{0} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.868 |
|
| \begin{align*}
t y^{\prime }&=2 y-t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.784 |
|
| \begin{align*}
t y^{\prime }&=2 y-t \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
✓ |
14.329 |
|
| \begin{align*}
t y^{\prime }+y&=\ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.153 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.309 |
|
| \begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.477 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.720 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.114 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.145 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.524 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.482 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
y^{\prime }&=y+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.600 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.022 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.296 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.191 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.511 |
|
| \begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.493 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
81.775 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.564 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
y^{\prime }&=y t +t +y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.372 |
|
| \begin{align*}
y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.148 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.278 |
|
| \begin{align*}
y^{\prime }&=-4 y t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.008 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }&=4 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.372 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 y t +6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.016 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -y}{t -6 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.609 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 y t +6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.307 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.131 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{i \omega t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.249 |
|
| \begin{align*}
y^{\prime }-a y&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.134 |
|
| \begin{align*}
y^{2}-1+x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.536 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=y-x +8 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.917 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.248 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.861 |
|
| \begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.324 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.974 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.327 |
|
| \begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.391 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.695 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.764 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.377 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.834 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.024 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
34.611 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.578 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.760 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.602 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.826 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.938 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.672 |
|
| \begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.880 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.731 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
25.421 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.450 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.296 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.597 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.850 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
21.074 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.616 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.336 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.826 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.670 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
61.079 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.036 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.059 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (1\right ) &= {\frac {5}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.238 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.704 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.910 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| \begin{align*}
x y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.710 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.817 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.145 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.648 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x \cos \left (x \right )+\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.230 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
60.362 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.950 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x -3} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.717 |
|
| \begin{align*}
2 x y y^{\prime }-1-y^{2}&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.188 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| \begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.964 |
|
| \begin{align*}
y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.549 |
|
| \begin{align*}
y^{2}+6 x^{2} y+\left (2 y x +2 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
35.579 |
|
| \begin{align*}
y+3 x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| \begin{align*}
1-x^{2}+2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.566 |
|
| \begin{align*}
3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.894 |
|
| \begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.060 |
|
| \begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
89.436 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.428 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=x^{4}+3 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{a x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| \begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.418 |
|
| \begin{align*}
x^{\prime }-\frac {2 x}{y}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.639 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.421 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }+y&=5 \left (x -2\right )^{2} \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.454 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.609 |
|
| \begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
12.579 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.523 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.638 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.349 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.695 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.928 |
|
| \begin{align*}
2 x +3 y+\left (y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.335 |
|
| \begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.125 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.147 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.303 |
|
| \begin{align*}
x^{2}-y^{2}-\frac {2 y^{3} y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
85.551 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.961 |
|
| \begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.015 |
|
| \begin{align*}
-x y^{\prime }+y&=a y^{2}+a y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.030 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
129.173 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
97.901 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.572 |
|
| \begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.567 |
|
| \begin{align*}
x -2 y+1&=\left (x -2 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.544 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.650 |
|
| \begin{align*}
y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.448 |
|
| \begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.077 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.856 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.726 |
|
| \begin{align*}
y&=x y^{\prime }+y^{\prime }-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.705 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.582 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| \begin{align*}
2 x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.747 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\
y \left (1\right ) &= \ln \left (2\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.232 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.483 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| \begin{align*}
x y y^{\prime }&=2 y^{2}-3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.950 |
|
| \begin{align*}
x y^{2}+x^{2} y y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.339 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.361 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.607 |
|
| \begin{align*}
x y^{\prime }&=y \tan \left (\ln \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.801 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.137 |
|
| \begin{align*}
x y^{\prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.937 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.979 |
|
| \begin{align*}
x -y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.803 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.505 |
|
| \begin{align*}
x y^{\prime }+1&={\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
x y^{2} y^{\prime }+y^{3}&=\frac {1}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| \begin{align*}
3 x^{2}-8 y x +2 y^{2}-\left (4 x^{2}-4 y x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.536 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.317 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.981 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.964 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.191 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
y^{\prime }&=y-x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.523 |
|
| \begin{align*}
1+y^{2}&=x y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.751 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
x^{2} y^{2}+1+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }+1&=\frac {\left (x +y\right )^{m}}{\left (x +y\right )^{n}+\left (x +y\right )^{p}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.855 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\
y \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.431 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=x \tan \left (x \right )+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\
y \left (\infty \right ) &= 2 \pi \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
3.743 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\
y \left (-\infty \right ) &= \frac {7 \pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
4.450 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.563 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.069 |
|
| \begin{align*}
4 x^{2}-y x +y^{2}+y^{\prime } \left (x^{2}-y x +4 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.755 |
|
| \begin{align*}
4 x^{2}+y x -3 y^{2}+y^{\prime } \left (-5 x^{2}+2 y x +y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.140 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.879 |
|
| \begin{align*}
2 x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.559 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.296 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+y^{\prime } \left (b \,x^{2}+2 c x y+f y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
124.392 |
|
| \begin{align*}
\left (y^{4}-3 x^{2}\right ) y^{\prime }&=-y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.483 |
|
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.953 |
|
| \begin{align*}
3 x +y-2+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
58.395 |
|
| \begin{align*}
y+y \sqrt {x^{2} y^{4}+1}+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| \begin{align*}
4 x y^{2}+\left (3 x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.910 |
|
| \begin{align*}
x +y^{3}+\left (3 y^{5}-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| \begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.624 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.622 |
|
| \begin{align*}
y^{3} y^{\prime }+3 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.871 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.074 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
\left (x^{2}+2 x -1\right ) y^{\prime }-\left (x +1\right ) y&=x -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=x^{3} \left (3 \ln \left (x \right )-1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime }+y x&=a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| \begin{align*}
2 x y^{\prime }-y&=3 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.082 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-\left (x +1\right )^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.720 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.157 |
|
| \begin{align*}
8 x y^{\prime }-y&=-\frac {1}{y^{3} \sqrt {x +1}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.224 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{-y^{2}-a^{2}+x^{2}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.010 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x +1}&=-\frac {\left (x +1\right )^{3} y^{3}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+y&=x^{2} \left (2 x -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.671 |
|
| \begin{align*}
\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
30.147 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
x +y y^{\prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.819 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| \begin{align*}
3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.014 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.436 |
|
| \begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.690 |
|
| \begin{align*}
y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.598 |
|
| \begin{align*}
y-y^{3}+\left (2 x y^{2}-x -a y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.781 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
63.154 |
|
| \begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-2 y x +6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.979 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.155 |
|
| \begin{align*}
2 y^{\prime }+y^{2}+\frac {1}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.229 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.818 |
|
| \begin{align*}
2 y^{2}-y x -\left (x^{2}-y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.037 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.414 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| \begin{align*}
y^{\prime }&=\tan \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.321 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.459 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.799 |
|
| \begin{align*}
y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.790 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.335 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.127 |
|
| \begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.922 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| \begin{align*}
2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| \begin{align*}
x^{2} y^{n} y^{\prime }&=2 x y^{\prime }-y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.619 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.464 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
101.651 |
|
| \begin{align*}
x^{\prime }&=t +x \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
x y^{\prime }&=x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
3 y^{\prime }&=\frac {4 x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| \begin{align*}
x \sin \left (y\right ) y^{\prime }&=\cos \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.945 |
|
| \begin{align*}
x y^{2} y^{\prime }&=y+1 \\
y \left (3 \,{\mathrm e}^{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (y+2\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.835 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
2 y+y^{\prime }&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| \begin{align*}
y^{\prime }-2 y&=-8 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \begin{align*}
y^{\prime }+3 y&=5 \,{\mathrm e}^{2 x}-6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{4 x} \\
y \left (0\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x +1}&=3 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }+\frac {5 y}{9 x}&=3 x^{3}+x \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
2 \cos \left (x +y\right )-2 x \sin \left (x +y\right )-2 x \sin \left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
4.876 |
|
| \begin{align*}
4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.802 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}-\frac {y \,{\mathrm e}^{\frac {y}{x}}}{x}+{\mathrm e}^{\frac {y}{x}} y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.619 |
|
| \begin{align*}
x \cos \left (x -2 y\right )+\sin \left (x -2 y\right )-2 x \cos \left (x -2 y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
7.454 |
|
| \begin{align*}
{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}-1\right ) y^{\prime }&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
✗ |
✗ |
1.965 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.130 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=-\frac {1}{y^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.450 |
|
| \begin{align*}
2 y^{2}-9 y x +\left (3 y x -6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.391 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}}-\frac {y}{x}+1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.650 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.622 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{2 x}-\frac {y}{x}-\frac {4}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.398 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.646 |
|
| \begin{align*}
x y^{\prime }&=x \cos \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.464 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {1}{x^{4} y^{{3}/{4}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.013 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.668 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
269.159 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-x}+y+{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+y}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.090 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y-9}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.551 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+x +7}{-2 x +y-9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.556 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -5 y-9}{-4 x +y+9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.109 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x -y\right ) \\
y \left (3\right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
y^{\prime }&=-y+{\mathrm e}^{x} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.870 |
|
| \begin{align*}
2 y^{\prime }+2 y&=x +3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.293 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
y^{\prime }+1&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.418 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y^{\prime }&=\frac {y-3 x}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.222 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.907 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
\sqrt {1+y^{2}}&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.031 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.161 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.710 |
|
| \begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
y^{\prime }&=\sqrt {4 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
x +2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.902 |
|
| \begin{align*}
y^{2}-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.074 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.127 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.556 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.550 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.446 |
|
| \begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.047 |
|
| \begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.814 |
|
| \begin{align*}
x y^{\prime }&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✗ |
✓ |
✓ |
863.770 |
|
| \begin{align*}
y+\sqrt {y x}&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.526 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.101 |
|
| \begin{align*}
2 x -4 y+1+\left (-3+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.234 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.005 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.279 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.993 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.506 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.654 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.667 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +1}+\tan \left (\frac {y-2 x}{x +1}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.752 |
|
| \begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| \begin{align*}
y+x \left (1+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.783 |
|
| \begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
5.768 |
|
| \begin{align*}
y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.911 |
|
| \begin{align*}
2 x y^{\prime }+y&=y^{2} \sqrt {x -x^{2} y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
8.512 |
|
| \begin{align*}
\frac {2 x y y^{\prime }}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
17.480 |
|
| \begin{align*}
2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.661 |
|
| \begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| \begin{align*}
x \left (y^{\prime }-y\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.379 |
|
| \begin{align*}
y&=x \left (y^{\prime }-x \cos \left (x \right )\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }&=2 x \left (x^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.153 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
\left (2 \,{\mathrm e}^{y}-x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }&=y+4 \ln \left (y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{3 x -y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.349 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| \begin{align*}
x y y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
x y^{\prime }-2 x^{2} \sqrt {y}&=4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
\left (2 x^{2} y \ln \left (y\right )-x \right ) y^{\prime }&=y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| \begin{align*}
\left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
x \left ({\mathrm e}^{y}-y^{\prime }\right )&=2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.834 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +x^{2} y^{2}&=4 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.691 |
|
| \begin{align*}
3 y^{\prime }+y^{2}+\frac {2}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.141 |
|
| \begin{align*}
x y^{\prime }-\left (2 x +1\right ) y+y^{2}&=-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
y^{\prime }-2 y x +y^{2}&=-x^{2}+5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.125 |
|
| \begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.755 |
|
| \begin{align*}
{\mathrm e}^{-y}-\left (2 y+x \,{\mathrm e}^{-y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
2.014 |
|
| \begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )-\sqrt {x^{2}-y}\, y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.167 |
|
| \begin{align*}
x^{2}+y^{2}+x +y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \begin{align*}
x^{2}+y+y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| \begin{align*}
y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.093 |
|
| \begin{align*}
y-\frac {1}{x}+\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
11.689 |
|
| \begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| \begin{align*}
y x&=\left (y^{3}+x^{2} y+x^{2}\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
x^{2} y \left (x y^{\prime }+y\right )&=x y^{\prime }+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.188 |
|
| \begin{align*}
x^{2}-y^{2}+y+x \left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.500 |
|
| \begin{align*}
2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.585 |
|
| \begin{align*}
\left (2 x^{2} y^{3}-1\right ) y+\left (4 x^{2} y^{3}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.493 |
|
| \begin{align*}
x \left (\ln \left (y\right )+2 \ln \left (x \right )-1\right ) y^{\prime }&=2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
5.312 |
|
| \begin{align*}
x^{2} y^{3}+y+\left (x^{3} y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| \begin{align*}
y^{2} \left (y-2 x y^{\prime }\right )&=x^{3} \left (x y^{\prime }-2 y\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
19.677 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.061 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-4}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.704 |
|
| \begin{align*}
y^{\prime }&=2+\left (y-2 x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +2 y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
58.089 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.701 |
|
| \begin{align*}
2 x y^{\prime }-y&=y^{\prime } \ln \left (y y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
31.902 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.619 |
|
| \begin{align*}
y&=x y^{\prime }-y^{\prime }-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
12.995 |
|
| \begin{align*}
2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.631 |
|
| \begin{align*}
x y^{\prime }+x^{2}+y x -y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
2 x y^{\prime }+y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.702 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.323 |
|
| \begin{align*}
y-y^{\prime }&=x y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.337 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
12.625 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.706 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.305 |
|
| \begin{align*}
y+y^{\prime } \ln \left (y\right )^{2}&=\left (x +2 \ln \left (y\right )\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.962 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.474 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
x -\frac {y}{y^{\prime }}&=\frac {2}{y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
94.040 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
151.775 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.649 |
|
| \begin{align*}
\frac {1}{x}&=\left (\frac {1}{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
47.875 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{y}+2 y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
2 \left (x -y^{2}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.721 |
|
| \begin{align*}
y^{\prime }+y x -x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.389 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{2} \left (2 x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.921 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{y y^{\prime }+x}&=2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.676 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.262 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.539 |
|
| \begin{align*}
y \left (-x y^{\prime }+y\right )&=\sqrt {y^{4}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.915 |
|
| \begin{align*}
x y^{\prime }+y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
79.418 |
|
| \begin{align*}
x^{2} \left (y^{\prime }-1\right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.744 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.359 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.534 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.358 |
|
| \begin{align*}
y^{2} \left (-x y^{\prime }+y\right )&=x^{3} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.305 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y-3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.030 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 x y \ln \left (x \right )+1&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \begin{align*}
x y^{\prime }&=x \sqrt {y-x^{2}}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| \begin{align*}
\left (2 x \,{\mathrm e}^{y}+y^{4}\right ) y^{\prime }&=y \,{\mathrm e}^{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.115 |
|
| \begin{align*}
x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.231 |
|
| \begin{align*}
y y^{\prime }&=4 x +3 y-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.055 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.425 |
|
| \begin{align*}
y^{\prime }&=\left (2 x -y\right )^{{1}/{3}}+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.047 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.211 |
|
| \begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
15.959 |
|
| \begin{align*}
2 x +3 y-1+\left (4 x +6 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.722 |
|
| \begin{align*}
2 x y^{\prime }+y+x y^{2} \left (x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.570 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
y y^{\prime }+y x&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.792 |
|
| \begin{align*}
\left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
625.926 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
178.191 |
|
| \begin{align*}
x y^{\prime }&=x^{2} {\mathrm e}^{-y}+2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.958 |
|
| \begin{align*}
y^{\prime }&=3 x +\sqrt {y-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
127.893 |
|
| \begin{align*}
x y^{\prime }-2 y+x y^{2} \left (2 x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.717 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y+1\right )^{2}}{x \left (y+1\right )-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.877 |
|
| \begin{align*}
\left (y-2 x y^{\prime }\right )^{2}&=4 y {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
31.641 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x}}{2}+y^{{1}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.911 |
|
| \begin{align*}
2 x y^{\prime }+1&=y+\frac {x^{2}}{-1+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.898 |
|
| \begin{align*}
y^{2} \left (x -1\right )&=x \left (y x +x -2 y\right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
11.883 |
|
| \begin{align*}
\left (x y^{\prime }-y\right )^{2}&=x^{2} y^{2}-x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
11.392 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|