| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=1+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \begin{align*}
2 x y^{\prime }&=y+2 x \cos \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \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*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.505 |
|
| \begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| \begin{align*}
x y^{\prime }+6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| \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*}
x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.982 |
|
| \begin{align*}
2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
3.498 |
|
| \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*}
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] |
✓ |
✓ |
✓ |
✗ |
0.441 |
|
| \begin{align*}
2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.066 |
|
| \begin{align*}
x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.086 |
|
| \begin{align*}
1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
23.193 |
|
| \begin{align*}
\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.642 |
|
| \begin{align*}
x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.060 |
|
| \begin{align*}
3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.717 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
8.814 |
|
| \begin{align*}
\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✗ |
✗ |
7.143 |
|
| \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*}
x y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.804 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=4 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.726 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x +y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.415 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.862 |
|
| \begin{align*}
y y^{\prime \prime }&=3 {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.642 |
|
| \begin{align*}
y^{\prime }&=f \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.114 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \ln \left (y\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.595 |
|
| \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 }&=-\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.556 |
|
| \begin{align*}
y^{\prime }+2 y x&=1+x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
y&=x y^{\prime }-\frac {{y^{\prime }}^{2}}{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
r y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.644 |
|
| \begin{align*}
x^{\prime }&=x-x^{2} \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
x^{\prime }&=10 x-x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \begin{align*}
x^{\prime }&=1-x^{2} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.721 |
|
| \begin{align*}
x^{\prime }&=9-4 x^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.273 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
x^{\prime }&=4 x \left (7-x\right ) \\
x \left (0\right ) &= 11 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
x^{\prime }&=7 x \left (x-13\right ) \\
x \left (0\right ) &= 17 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \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*}
2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.314 |
|
| \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*}
6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.791 |
|
| \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*}
{\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.700 |
|
| \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*}
\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| \begin{align*}
x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.431 |
|