|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{2} y^{\prime } = x \left (y-1\right )+\left (y-1\right )^{2} \] |
riccati, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.263 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.122 |
|
|
\[ {}y^{\prime } = 1-x^{5}+\sqrt {x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.189 |
|
|
\[ {}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0 \] |
exact, linear, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.938 |
|
|
\[ {}{\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime } = 0 \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-x^{2} y^{2} = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = \frac {-2 x +y}{x} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.744 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.392 |
|
|
\[ {}y^{\prime }+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.247 |
|
|
\[ {}y^{\prime }+y = x^{2}+2 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.616 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.106 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -2 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.099 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.107 |
|
|
\[ {}x y^{\prime } = x +y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.824 |
|
|
\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.474 |
|
|
\[ {}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime } = x +\frac {1}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.277 |
|
|
\[ {}x y^{\prime }+2 y = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.03 |
|
|
\[ {}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.279 |
|
|
\[ {}x y y^{\prime } = \left (1+x \right ) \left (y+1\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.736 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{y+2 x} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.978 |
|
|
\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.057 |
|
|
\[ {}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.185 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.556 |
|
|
\[ {}\left (x +y^{2}\right ) y^{\prime }-x^{2}+y = 0 \] |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
68.71 |
|
|
\[ {}y y^{\prime } = x \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime }-y = x^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.89 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.938 |
|
|
\[ {}y^{\prime }+y \ln \left (x \right ) = x^{-x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}x y^{\prime }+y = x \] |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.986 |
|
|
\[ {}-y+x y^{\prime } = x^{3} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.661 |
|
|
\[ {}x y^{\prime }+n y = x^{n} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.861 |
|
|
\[ {}x y^{\prime }-n y = x^{n} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.794 |
|
|
\[ {}\left (x^{3}+x \right ) y^{\prime }+y = x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.812 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.232 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.333 |
|
|
\[ {}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.52 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.105 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y = \sin \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.73 |
|
|
\[ {}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.109 |
|
|
\[ {}y^{\prime } \sin \left (x \right )+y = \sin \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.414 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.059 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.352 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.551 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.407 |
|
|
\[ {}3 y^{2} y^{\prime } = 2 x -1 \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
9.704 |
|
|
\[ {}y^{\prime } = 6 x y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.619 |
|
|
\[ {}y^{\prime } = x \sec \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.799 |
|
|
\[ {}y^{\prime } = 3 \cos \left (y\right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.3 |
|
|
\[ {}x y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.723 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
exact, linear, separable, differentialType, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.889 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}x^{2} y^{\prime }-y^{2} = 0 \] |
exact, riccati, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.083 |
|
|
\[ {}y^{\prime }+2 x y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\cot \left (x \right ) y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.666 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}y^{\prime }-2 x y = 2 x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.415 |
|
|
\[ {}x y^{\prime } = x y+y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.151 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.683 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.685 |
|
|
\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.056 |
|
|
\[ {}2 x y^{\prime } = 1-y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.274 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = x y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.834 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.848 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.822 |
|
|
\[ {}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.122 |
|
|
\[ {}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.906 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+x y y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.035 |
|
|
\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.959 |
|
|
\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.107 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
homogeneousTypeD, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.435 |
|
|
\[ {}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
riccati, homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.807 |
|
|
\[ {}y^{\prime } = \sin \left (x -y+1\right )^{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.507 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.974 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.003 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.217 |
|
|
\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
33.48 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
1.237 |
|
|
\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.05 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
38.22 |
|
|
\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \] |
exact |
[_exact] |
✓ |
✓ |
7.582 |
|
|
\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.973 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.994 |
|
|
\[ {}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
31.98 |
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\[ {}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \] |
exact, riccati |
[_exact, _rational, _Riccati] |
✓ |
✓ |
1.38 |
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\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.34 |
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