|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 1-2 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.267 |
|
|
\[ {}y^{\prime } = 4 y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.139 |
|
|
\[ {}y^{\prime } = 2 y \left (1-y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.771 |
|
|
\[ {}y^{\prime } = y+t +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime } = 3 y \left (1-y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime } = 2 y-t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.857 |
|
|
\[ {}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (t +y\right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.829 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.127 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.45 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.099 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.278 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.711 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.726 |
|
|
\[ {}y^{\prime } = y^{2}+y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.515 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.265 |
|
|
\[ {}y^{\prime } = y^{3}+y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.534 |
|
|
\[ {}y^{\prime } = -t^{2}+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.132 |
|
|
\[ {}y^{\prime } = t y+t y^{2} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime } = t^{2}+t^{2} y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.767 |
|
|
\[ {}y^{\prime } = t +t y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = t^{2}-2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.138 |
|
|
\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.468 |
|
|
\[ {}\theta ^{\prime } = 2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.107 |
|
|
\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.388 |
|
|
\[ {}v^{\prime } = -\frac {v}{R C} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.605 |
|
|
\[ {}v^{\prime } = \frac {K -v}{R C} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}v^{\prime } = 2 V \left (t \right )-2 v \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.263 |
|
|
\[ {}y^{\prime } = t -y^{2} \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
4.531 |
|
|
\[ {}y^{\prime } = y^{2}-4 t \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
6.278 |
|
|
\[ {}y^{\prime } = \sin \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.774 |
|
|
\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.837 |
|
|
\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.847 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime } = y^{2}-y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.622 |
|
|
\[ {}y^{\prime } = 2 y^{3}+t^{2} \] |
abelFirstKind |
[_Abel] |
❇ |
N/A |
0.441 |
|
|
\[ {}y^{\prime } = \sqrt {y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.447 |
|
|
\[ {}y^{\prime } = 2-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.405 |
|
|
\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.905 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.234 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.785 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.087 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.138 |
|
|
\[ {}y^{\prime } = y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.253 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.741 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (y+2\right )^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime } = \frac {t}{y-2} \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.28 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.872 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.544 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.235 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.588 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.245 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.575 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.8 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.705 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.263 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.446 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.551 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.211 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.852 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.832 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.873 |
|
|
\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime } = \frac {1}{y-2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.368 |
|
|
\[ {}v^{\prime } = -v^{2}-2 v-2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.539 |
|
|
\[ {}y^{\prime } = 1+\cos \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.327 |
|
|
\[ {}y^{\prime } = \tan \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime } = y \ln \left ({| y|}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.523 |
|
|
\[ {}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.748 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.293 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime } = y-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.533 |
|
|
\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.753 |
|
|
\[ {}y^{\prime } = y^{3}-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.621 |
|
|
\[ {}y^{\prime } = \cos \left (\frac {\pi y}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.612 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.345 |
|
|
\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.128 |
|
|
\[ {}y^{\prime } = y^{2}-y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.306 |
|
|
\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime } = -3 y+4 \cos \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.989 |
|
|
\[ {}y^{\prime } = 2 y+\sin \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.639 |
|
|
\[ {}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.96 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime }+3 y = \cos \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime }+2 y = 3 t^{2}+2 t -1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.668 |
|
|
|
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