| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.372 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\
y \left (\pi \right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.421 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
y \left (0\right ) &= \operatorname {y0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.223 |
|
| \begin{align*}
y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+y \,{\mathrm e}^{x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.154 |
|
| \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 }-y&=\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.022 |
|
| \begin{align*}
y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.362 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\sin \left (x \right )} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
10.178 |
|
| \begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.470 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
1.139 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\ln \left (y x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
3.995 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right ) y^{{1}/{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.861 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| \begin{align*}
y^{\prime }&=\ln \left (1+x^{2}+y^{2}\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.281 |
|
| \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^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
3.092 |
|
| \begin{align*}
y^{\prime }&=x \left (y^{2}-1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.487 |
|
| \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 }&=y^{{2}/{5}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.977 |
|
| \begin{align*}
y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
46.484 |
|
| \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} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \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 }+y&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
7 x y^{\prime }-2 y&=-\frac {x^{2}}{y^{6}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
0.375 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\frac {1}{\left (x^{2}+1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime }-2 y&=x y^{3} \\
y \left (0\right ) &= 2 \sqrt {2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y^{\prime }-y x&=x y^{{3}/{2}} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.500 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{4} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }-2 y&=2 \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.046 |
|
| \begin{align*}
y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{3} \\
y \left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
y^{\prime }-y&=x \sqrt {y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
1.049 |
|
| \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 y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.748 |
|
| \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*}
y^{\prime }&=\frac {y^{2}+y \tan \left (x \right )+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.243 |
|
| \begin{align*}
x \ln \left (x \right )^{2} y^{\prime }&=-4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.638 |
|
| \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*}
\left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime }&=2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.457 |
|
| \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*}
6 x^{2} y^{2}+4 x^{3} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
3 \cos \left (x \right ) y+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
61.855 |
|
| \begin{align*}
14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
2 x -2 y^{2}+\left (12 y^{2}-4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.480 |
|
| \begin{align*}
\left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \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 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 \cos \left (x \right ) y+9 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
27.067 |
|
| \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*}
3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.700 |
|
| \begin{align*}
2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
2.958 |
|
| \begin{align*}
\frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.315 |
|
| \begin{align*}
y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
5.747 |
|
| \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}^{x} \left (x^{2} y^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.449 |
|
| \begin{align*}
x^{2} {\mathrm e}^{x^{2}+y} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{x^{2}+y}-12 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.535 |
|
| \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*}
4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.530 |
|
| \begin{align*}
-4 \cos \left (x \right ) y+4 \sin \left (x \right ) \cos \left (x \right )+\sec \left (x \right )^{2}+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.685 |
|
| \begin{align*}
\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.284 |
|
| \begin{align*}
\sin \left (x \right )-y \sin \left (x \right )-2 \cos \left (x \right )+\cos \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.402 |
|
| \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 |
|