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) |
|
\[ {}y^{\prime } = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.122 |
|
|
\[ {}y^{\prime } = 1-x^{5}+\sqrt {x} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.189 |
|
|
\[ {}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.938 |
|
|
\[ {}{\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = \frac {-2 x +y}{x} \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.744 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.392 |
|
|
\[ {}y^{\prime }+y = 0 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.247 |
|
|
\[ {}y^{\prime }+y = x^{2}+2 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.616 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = x \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.106 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -2 y} \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.099 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.107 |
|
|
\[ {}x y^{\prime } = x +y \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.824 |
|
|
\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.474 |
|
|
\[ {}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime } = x +\frac {1}{x} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.277 |
|
|
\[ {}x y^{\prime }+2 y = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.03 |
|
|
\[ {}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.279 |
|
|
\[ {}x y y^{\prime } = \left (1+x \right ) \left (y+1\right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.736 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{y+2 x} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.978 |
|
|
\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.057 |
|
|
\[ {}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right ) \] |
1 |
1 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.185 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.556 |
|
|
\[ {}\left (x +y^{2}\right ) y^{\prime }-x^{2}+y = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
68.71 |
|
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