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) |
|
\[ {}3 y^{2} y^{\prime } = 2 x -1 \] |
1 |
1 |
3 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
9.704 |
|
|
\[ {}y^{\prime } = 6 x y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.619 |
|
|
\[ {}y^{\prime } = x \sec \left (y\right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.799 |
|
|
\[ {}y^{\prime } = 3 \cos \left (y\right )^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.3 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.723 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, differentialType, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.889 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}x^{2} y^{\prime }-y^{2} = 0 \] |
1 |
1 |
1 |
exact, riccati, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.083 |
|
|
\[ {}y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\cot \left (x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.666 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}y^{\prime }-2 x y = 2 x \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.415 |
|
|
\[ {}x y^{\prime } = x y+y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.151 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.683 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.685 |
|
|
\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
1 |
1 |
1 |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.056 |
|
|
\[ {}2 x y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.274 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = x y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.834 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.848 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.822 |
|
|
\[ {}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.122 |
|
|
\[ {}{\mathrm e}^{2 x} y y^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.906 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
1 |
1 |
2 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
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