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) |
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime }-y = x^{3} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = x \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.89 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.938 |
|
|
\[ {}y^{\prime }+y \ln \left (x \right ) = x^{-x} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.986 |
|
|
\[ {}-y+x y^{\prime } = x^{3} \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.661 |
|
|
\[ {}x y^{\prime }+n y = x^{n} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.861 |
|
|
\[ {}x y^{\prime }-n y = x^{n} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.794 |
|
|
\[ {}\left (x^{3}+x \right ) y^{\prime }+y = x \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.812 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = x \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.232 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.333 |
|
|
\[ {}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.52 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.105 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }+y = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.73 |
|
|
\[ {}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.109 |
|
|
\[ {}\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.414 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.059 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.352 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.551 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.407 |
|
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