| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.564 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.156 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
3.787 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \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 }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime }&=t^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime }&=1-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=t +y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=3 y \left (1-y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.267 |
|
| \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 (y+\frac {1}{2}\right ) \left (t +y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.829 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.912 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
20.250 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
19.204 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.746 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
59.471 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
17.478 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.192 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.285 |
|
| \begin{align*}
y^{\prime }&=-t^{2}+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \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 }&=t^{2}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.875 |
|
| \begin{align*}
\theta ^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.684 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
v^{\prime }&=\frac {K -v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
v^{\prime }&=2 V \left (t \right )-2 v \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.760 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime }&=t -y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.154 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.061 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.954 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.092 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.923 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.193 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.134 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
y \left (0\right ) &= {\frac {1}{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
12.944 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.131 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\theta \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
23.905 |
|
| \begin{align*}
y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.286 |
|
| \begin{align*}
y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.300 |
|
| \begin{align*}
y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.593 |
|
| \begin{align*}
y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.967 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| \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 {1}{\left (y+2\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{-2+y} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.544 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.698 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.586 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.853 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.296 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.279 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.582 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.229 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.605 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
25.070 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.758 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.017 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.077 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.038 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.006 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.982 |
|
| \begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.545 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{-2+y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
v^{\prime }&=-v^{2}-2 v-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
w^{\prime }&=3 w^{3}-12 w^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.692 |
|
| \begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| \begin{align*}
y^{\prime }&=y \ln \left ({| y|}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.327 |
|
| \begin{align*}
w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.194 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.044 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.865 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.892 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.877 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.695 |
|
| \begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.307 |
|
| \begin{align*}
y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.023 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| \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 |
|