| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.257 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.961 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.406 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.644 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
4.114 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \begin{align*}
y^{\prime }&=t^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \begin{align*}
y^{\prime }&=1-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.530 |
|
| \begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| \begin{align*}
y^{\prime }&=t +y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
y^{\prime }&=3 y \left (1-y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.601 |
|
| \begin{align*}
y^{\prime }&=2 y-t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime }&=\left (y+\frac {1}{2}\right ) \left (y+t \right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.024 |
|
| \begin{align*}
y^{\prime }&=\left (1+t \right ) y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.591 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
13.928 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
13.687 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.240 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
67.544 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
20.520 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.127 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.918 |
|
| \begin{align*}
y^{\prime }&=-t^{2}+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime }&=t y+t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.889 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.130 |
|
| \begin{align*}
y^{\prime }&=t +t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.716 |
|
| \begin{align*}
y^{\prime }&=t^{2}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.206 |
|
| \begin{align*}
\theta ^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.142 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.396 |
|
| \begin{align*}
v^{\prime }&=\frac {K -v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
v^{\prime }&=2 V \left (t \right )-2 v \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.752 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.633 |
|
| \begin{align*}
y^{\prime }&=t -y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.389 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.105 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
10.028 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.993 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.839 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.787 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.717 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
y \left (0\right ) &= {\frac {1}{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
21.290 |
|
| \begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
3.229 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.569 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.788 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\theta \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
28.075 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
6.482 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.255 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
8.497 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.249 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.658 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.454 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (1+y\right ) \left (-2+t \right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.536 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (2+y\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.916 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.711 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.005 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.730 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.349 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.379 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
2.171 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.240 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
2.043 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.508 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
24.747 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.998 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.495 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.568 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.842 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.638 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.076 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.645 |
|
| \begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.352 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
v^{\prime }&=-v^{2}-2 v-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
w^{\prime }&=3 w^{3}-12 w^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.022 |
|
| \begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
y^{\prime }&=y \ln \left ({| y|}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
28.061 |
|
| \begin{align*}
w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.359 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.215 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.836 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.104 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.140 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| \begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.690 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.393 |
|
| \begin{align*}
y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.743 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.850 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.869 |
|
| \begin{align*}
y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| \begin{align*}
y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.079 |
|