|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.362 |
|
|
\[ {}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.597 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = y-1 \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.071 |
|
|
\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.981 |
|
|
\[ {}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✗ |
32.723 |
|
|
\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.314 |
|
|
\[ {}x -y+x y^{\prime } = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.218 |
|
|
\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.031 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y+x^{2} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.745 |
|
|
\[ {}x y^{\prime } = y+\sqrt {-x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.697 |
|
|
\[ {}2 x^{2} y^{\prime } = x^{2}+y^{2} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.951 |
|
|
\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.026 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.454 |
|
|
\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \] |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.473 |
|
|
\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.897 |
|
|
\[ {}x +y-2+\left (-y+4+x \right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.743 |
|
|
\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.56 |
|
|
\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.536 |
|
|
\[ {}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.121 |
|
|
\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.97 |
|
|
\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.533 |
|
|
\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.838 |
|
|
\[ {}y \left (1+\sqrt {y^{4} x^{2}+1}\right )+2 x y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.709 |
|
|
\[ {}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.108 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{-x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.133 |
|
|
\[ {}x^{2}-x y^{\prime } = y \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.849 |
|
|
\[ {}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.074 |
|
|
\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.083 |
|
|
\[ {}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = 2 x \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.506 |
|
|
\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.51 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
9.075 |
|
|
\[ {}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.676 |
|
|
\[ {}\left (2 x -y^{2}\right ) y^{\prime } = 2 y \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.271 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.506 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.484 |
|
|
\[ {}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 2 x \,{\mathrm e}^{{\mathrm e}^{x}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.138 |
|
|
\[ {}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.222 |
|
|
\[ {}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.681 |
|
|
\[ {}y^{\prime }-y = -2 \,{\mathrm e}^{-x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.295 |
|
|
\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✗ |
N/A |
4.23 |
|
|
\[ {}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.698 |
|
|
\[ {}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✗ |
N/A |
2.308 |
|
|
\[ {}2 x y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✗ |
4.82 |
|
|
\[ {}x y^{\prime }+y = 2 x \] |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.009 |
|
|
\[ {}y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 1 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.679 |
|
|
\[ {}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = -\sin \left (2 x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.099 |
|
|
\[ {}y^{\prime }+2 x y = 2 x y^{2} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.732 |
|
|
\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.863 |
|
|
\[ {}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime }-2 \,{\mathrm e}^{x} y = 2 \sqrt {{\mathrm e}^{x} y} \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.112 |
|
|
\[ {}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
10.419 |
|
|
\[ {}2 y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
10.866 |
|
|
\[ {}\left (1+x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.496 |
|
|
\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.376 |
|
|
\[ {}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )} \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.112 |
|
|
\[ {}y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.427 |
|
|
\[ {}\cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 1+x \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.095 |
|
|
\[ {}y y^{\prime }+1 = \left (-1+x \right ) {\mathrm e}^{-\frac {y^{2}}{2}} \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.293 |
|
|
\[ {}y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
3.725 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.869 |
|
|
\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
1.825 |
|
|
\[ {}\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
30.911 |
|
|
\[ {}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
51.631 |
|
|
\[ {}2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \] |
exact, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
✓ |
2.423 |
|
|
\[ {}\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
11.772 |
|
|
\[ {}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
22.627 |
|
|
\[ {}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
37.151 |
|
|
\[ {}\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
41.57 |
|
|
\[ {}\frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
62.519 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.991 |
|
|
\[ {}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
2.072 |
|
|
\[ {}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.919 |
|
|
\[ {}1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}x^{2}+y-x y^{\prime } = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.183 |
|
|
\[ {}x +y^{2}-2 x y y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.652 |
|
|
\[ {}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.855 |
|
|
\[ {}x +\sin \left (x \right )+\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.541 |
|
|
\[ {}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational] |
✓ |
✓ |
1.615 |
|
|
\[ {}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
8.741 |
|
|
\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.676 |
|
|
\[ {}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.663 |
|
|
\[ {}4 {y^{\prime }}^{2}-9 x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.444 |
|
|
\[ {}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left ({\mathrm e}^{2 x}-1\right ) \] |
separable |
[_separable] |
✓ |
✓ |
1.556 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.635 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
2.367 |
|
|
\[ {}{y^{\prime }}^{2}-\left (y+2 x \right ) y^{\prime }+x^{2}+x y = 0 \] |
linear, quadrature |
[_quadrature] |
✓ |
✓ |
1.46 |
|
|
\[ {}{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y} = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
3.904 |
|
|
\[ {}{y^{\prime }}^{3} = y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.882 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.56 |
|
|
\[ {}{y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.668 |
|
|
\[ {}y = {y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.111 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.197 |
|
|
\[ {}x = \ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \] |
quadrature |
[_quadrature] |
✓ |
✗ |
5.153 |
|
|
\[ {}x = {y^{\prime }}^{2}-2 y^{\prime }+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.63 |
|
|
\[ {}y = y^{\prime } \ln \left (y^{\prime }\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.011 |
|
|
\[ {}y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.575 |
|
|
|
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|
|
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