|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 4 y^{2}
\] |
[_quadrature] |
✓ |
0.398 |
|
|
\[
{}y^{\prime } = 2 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
0.780 |
|
|
\[
{}y^{\prime } = y+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.831 |
|
|
\[
{}y^{\prime } = 3 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
1.108 |
|
|
\[
{}y^{\prime } = 2 y-t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.032 |
|
|
\[
{}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (y+t \right )
\] |
[_Riccati] |
✓ |
1.496 |
|
|
\[
{}y^{\prime } = \left (1+t \right ) y
\] |
[_separable] |
✓ |
1.428 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
1.309 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
1.296 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
1.212 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
1.139 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
1.206 |
|
|
\[
{}y^{\prime } = y^{2}+y
\] |
[_quadrature] |
✓ |
0.599 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
0.615 |
|
|
\[
{}y^{\prime } = y^{3}+y^{2}
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}y^{\prime } = -t^{2}+2
\] |
[_quadrature] |
✓ |
0.221 |
|
|
\[
{}y^{\prime } = t y+t y^{2}
\] |
[_separable] |
✓ |
1.983 |
|
|
\[
{}y^{\prime } = t^{2}+t^{2} y
\] |
[_separable] |
✓ |
0.961 |
|
|
\[
{}y^{\prime } = t +t y
\] |
[_separable] |
✓ |
0.932 |
|
|
\[
{}y^{\prime } = t^{2}-2
\] |
[_quadrature] |
✓ |
0.220 |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
0.606 |
|
|
\[
{}\theta ^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.390 |
|
|
\[
{}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
0.558 |
|
|
\[
{}v^{\prime } = -\frac {v}{R C}
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}v^{\prime } = \frac {K -v}{R C}
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}v^{\prime } = 2 V \left (t \right )-2 v
\] |
[[_linear, ‘class A‘]] |
✓ |
1.117 |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
0.589 |
|
|
\[
{}y^{\prime } = t -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.112 |
|
|
\[
{}y^{\prime } = y^{2}-4 t
\] |
[[_Riccati, _special]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
2.576 |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
0.738 |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
0.809 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
0.804 |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
1.481 |
|
|
\[
{}y^{\prime } = 2 y^{3}+t^{2}
\] |
[_Abel] |
✗ |
0.379 |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
0.627 |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
0.461 |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
1.038 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
2.632 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
1.797 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
4.108 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
2.581 |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
0.385 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
0.571 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )}
\] |
[_separable] |
✓ |
1.113 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (y+2\right )^{2}}
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } = \frac {t}{y-2}
\] |
[_separable] |
✓ |
1.935 |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
1.044 |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
1.085 |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
1.039 |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
1.082 |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
0.828 |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
0.847 |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
0.862 |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
0.816 |
|
|
\[
{}y^{\prime } = \cos \left (y\right )
\] |
[_quadrature] |
✓ |
0.855 |
|
|
\[
{}y^{\prime } = \cos \left (y\right )
\] |
[_quadrature] |
✓ |
2.155 |
|
|
\[
{}y^{\prime } = \cos \left (y\right )
\] |
[_quadrature] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = \cos \left (y\right )
\] |
[_quadrature] |
✓ |
0.895 |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
0.664 |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
0.738 |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
0.725 |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
0.746 |
|
|
\[
{}w^{\prime } = \left (1-w\right ) \sin \left (w\right )
\] |
[_quadrature] |
✓ |
3.595 |
|
|
\[
{}y^{\prime } = \frac {1}{y-2}
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}v^{\prime } = -v^{2}-2 v-2
\] |
[_quadrature] |
✓ |
0.425 |
|
|
\[
{}w^{\prime } = 3 w^{3}-12 w^{2}
\] |
[_quadrature] |
✓ |
0.670 |
|
|
\[
{}y^{\prime } = 1+\cos \left (y\right )
\] |
[_quadrature] |
✓ |
0.481 |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
0.485 |
|
|
\[
{}y^{\prime } = y \ln \left ({| y|}\right )
\] |
[_quadrature] |
✓ |
1.185 |
|
|
\[
{}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right )
\] |
[_quadrature] |
✓ |
1.033 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.660 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.578 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.653 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.660 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.651 |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
0.657 |
|
|
\[
{}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
0.646 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
0.657 |
|
|
\[
{}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
0.667 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
0.585 |
|
|
\[
{}y^{\prime } = \cos \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
1.367 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
0.612 |
|
|
\[
{}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
0.675 |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
0.623 |
|
|
\[
{}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.911 |
|
|
\[
{}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.912 |
|
|
\[
{}y^{\prime } = -3 y+4 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.146 |
|
|
\[
{}y^{\prime } = 2 y+\sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.129 |
|
|
\[
{}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.883 |
|
|
\[
{}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.173 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.211 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.334 |
|
|
\[
{}y^{\prime }+3 y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.369 |
|
|
\[
{}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.087 |
|
|
\[
{}y^{\prime }+2 y = 3 t^{2}+2 t -1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.927 |
|
|
\[
{}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.645 |
|