| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=x \left (y-4\right )^{2}-2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
96.562 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.906 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.147 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime }&=\left (-2+y\right )^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y^{\prime }&=10+3 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.110 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| \begin{align*}
y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.684 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y-6 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.942 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y-6 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.260 |
|
| \begin{align*}
y^{\prime }&=\sin \left (5 x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
1+{\mathrm e}^{3 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime }-\left (-1+y\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime } x&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.231 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.050 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.630 |
|
| \begin{align*}
y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (1+y\right )^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.431 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.872 |
|
| \begin{align*}
\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.965 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.809 |
|
| \begin{align*}
\left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.638 |
|
| \begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.875 |
|
| \begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (\cos \left (x \right ) x +\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.618 |
|
| \begin{align*}
y^{\prime }&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.141 |
|
| \begin{align*}
y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x -3} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.982 |
|
| \begin{align*}
2 y y^{\prime } x -1-y^{2}&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.793 |
|
| \begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.163 |
|
| \begin{align*}
2 x y \left (4-y^{2}\right )+\left (-1+y\right ) \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.540 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| \begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.966 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.056 |
|
| \begin{align*}
y x -x +\left (y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| \begin{align*}
y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.092 |
|
| \begin{align*}
2 x \cos \left (y\right )-{\mathrm e}^{x}-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.711 |
|
| \begin{align*}
3 x^{2}+3 x y^{2}+\left (3 x^{2} y-3 y^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.536 |
|
| \begin{align*}
y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.547 |
|
| \begin{align*}
\frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.373 |
|
| \begin{align*}
y+3 x +y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.983 |
|
| \begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.049 |
|
| \begin{align*}
6 x +y^{2}+\left (2 y x -3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.485 |
|
| \begin{align*}
1-x^{2}+2 y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| \begin{align*}
3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.258 |
|
| \begin{align*}
y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.507 |
|
| \begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.339 |
|
| \begin{align*}
2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
x^{3}+y^{4} x +2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
43.327 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
y^{\prime }-2 y&=\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.083 |
|
| \begin{align*}
y^{\prime }-2 y x&=6 y \,{\mathrm e}^{y^{2}} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
44.191 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=x^{4}+3 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.621 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) x&=\cot \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.719 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.875 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{a x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| \begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.197 |
|
| \begin{align*}
x^{\prime }-\frac {2 x}{y}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.143 |
|
| \begin{align*}
y y^{\prime }+y^{2} \cot \left (x \right )&=\csc \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| \begin{align*}
y^{\prime } x +y&=3 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.949 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
8.667 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.131 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.892 |
|
| \begin{align*}
y^{\prime } x +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‘]] |
✓ |
✓ |
✓ |
✓ |
6.857 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.792 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.101 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.387 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.802 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.622 |
|
| \begin{align*}
2 x +3 y+\left (y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.691 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.845 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.373 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.776 |
|
| \begin{align*}
x^{2}-y^{2}-\frac {2 y^{3} y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.888 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
14.080 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.674 |
|
| \begin{align*}
y-y^{\prime } x&=a y^{2}+a y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.406 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.510 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
69.837 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.667 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.131 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
6.361 |
|
| \begin{align*}
y^{\prime } x +y&=y y^{\prime } x -y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.725 |
|
| \begin{align*}
2 y y^{\prime } x +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
x -2 y+1&=\left (x -2 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.673 |
|
| \begin{align*}
\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.717 |
|
| \begin{align*}
\cos \left (x \right ) y-2 \sin \left (y\right )&=\left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime } \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
14.220 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.660 |
|