| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.634 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.008 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
4.682 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.212 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y^{\prime }&=t^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
y^{\prime }&=1-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| \begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
y^{\prime }&=t +y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
y^{\prime }&=3 y \left (1-y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.243 |
|
| \begin{align*}
y^{\prime }&=2 y-t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
y^{\prime }&=\left (y+\frac {1}{2}\right ) \left (y+t \right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.145 |
|
| \begin{align*}
y^{\prime }&=\left (1+t \right ) y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
17.604 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
17.295 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.673 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
17.738 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
17.214 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.630 |
|
| \begin{align*}
y^{\prime }&=-t^{2}+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
y^{\prime }&=t y+t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.967 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
y^{\prime }&=t +t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.365 |
|
| \begin{align*}
y^{\prime }&=t^{2}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.991 |
|
| \begin{align*}
\theta ^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.327 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
v^{\prime }&=\frac {K -v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
v^{\prime }&=2 V \left (t \right )-2 v \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.436 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime }&=t -y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.011 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.164 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.283 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.724 |
|
| \begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.626 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.815 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.631 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
y \left (0\right ) &= {\frac {1}{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
11.691 |
|
| \begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
0.916 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.919 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\theta \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
27.807 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
2.383 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.457 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
2.637 |
|
| \begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
1.413 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
29.974 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (1+y\right ) \left (-2+t \right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.873 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (2+y\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.158 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.047 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.807 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.804 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.344 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y-12 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.743 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.811 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
25.457 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.858 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= \pi \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
0.743 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.690 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.852 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.827 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.830 |
|
| \begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.840 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
v^{\prime }&=-v^{2}-2 v-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
w^{\prime }&=3 w^{3}-12 w^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.320 |
|
| \begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.999 |
|
| \begin{align*}
y^{\prime }&=y \ln \left ({| y|}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.896 |
|
| \begin{align*}
w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.584 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.676 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.565 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.534 |
|
| \begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.979 |
|
| \begin{align*}
y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.971 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.395 |
|
| \begin{align*}
y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \begin{align*}
y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|