Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = t^{2}+3 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.073 |
|
|
\[ {}y^{\prime } = t \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.097 |
|
|
\[ {}y^{\prime } = \sin \left (3 t \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.154 |
|
|
\[ {}y^{\prime } = \sin \left (t \right )^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.213 |
|
|
\[ {}y^{\prime } = \frac {t}{t^{2}+4} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.089 |
|
|
\[ {}y^{\prime } = \ln \left (t \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.171 |
|
|
\[ {}y^{\prime } = \frac {t}{\sqrt {t}+1} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.242 |
|
|
\[ {}y^{\prime } = 2 y-4 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.346 |
|
|
\[ {}y^{\prime } = -y^{3} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.267 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.207 |
|
|
\[ {}y^{\prime } = t \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.204 |
|
|
\[ {}y^{\prime } = \sin \left (t \right )^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.236 |
|
|
\[ {}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.22 |
|
|
\[ {}y^{\prime } = \frac {y}{t} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.25 |
|
|
\[ {}y^{\prime } = y-1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.119 |
|
|
\[ {}y^{\prime } = 1-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.121 |
|
|
\[ {}y^{\prime } = y^{3}-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.237 |
|
|
\[ {}y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.12 |
|
|
\[ {}y^{\prime } = \left (t^{2}+1\right ) y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.48 |
|
|
\[ {}y^{\prime } = -y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.089 |
|
|
\[ {}y^{\prime } = 2 y+{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.663 |
|
|
\[ {}y^{\prime } = 2 y+{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.45 |
|
|
\[ {}y^{\prime } = t -y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.454 |
|
|
\[ {}t y^{\prime }+2 y = \sin \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.637 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime } = y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.191 |
|
|
\[ {}y^{\prime } = 2 y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.226 |
|
|
\[ {}t y^{\prime } = y+t^{3} \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime } = \frac {2 y}{t +1} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.977 |
|
|
\[ {}t y^{\prime } = -y+t^{3} \] |
1 |
1 |
1 |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.954 |
|
|
\[ {}t \ln \left (t \right ) y^{\prime } = \ln \left (t \right ) t -y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = \frac {2 y}{-t^{2}+1}+3 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.002 |
|
|
\[ {}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.224 |
|
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