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) |
|
\[ {}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.764 |
|
|
\[ {}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )} \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.517 |
|
|
\[ {}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0 \] |
1 |
2 |
2 |
separable |
[_separable] |
✓ |
✓ |
1.059 |
|
|
\[ {}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
1.894 |
|
|
\[ {}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0 \] |
1 |
2 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.494 |
|
|
\[ {}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0 \] |
1 |
2 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.391 |
|
|
\[ {}x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
1 |
2 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime }+\frac {x}{y}+2 = 0 \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.401 |
|
|
\[ {}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.013 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.566 |
|
|
\[ {}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.218 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.681 |
|
|
\[ {}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0 \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.858 |
|
|
\[ {}x^{2}-x y+y^{2}-x y y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.362 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = \frac {2 x +y-1}{x -y-2} \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.213 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.103 |
|
|
\[ {}y^{\prime } = \sin \left (x -y\right )^{2} \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.862 |
|
|
\[ {}y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \] |
1 |
1 |
1 |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.57 |
|
|
\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
exact |
[_exact, _rational] |
✓ |
✓ |
1.747 |
|
|
\[ {}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.895 |
|
|
\[ {}x y^{2}+x -2 y+3+\left (x^{2} y-2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
exact, first_order_ode_lie_symmetry_calculated |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.205 |
|
|
\[ {}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact |
[_exact] |
✓ |
✓ |
32.388 |
|
|
\[ {}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 x y-y \sin \left (2 x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
33.93 |
|
|
\[ {}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.705 |
|
|
\[ {}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.751 |
|
|
\[ {}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
homogeneousTypeD2, exactWithIntegrationFactor |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.152 |
|
|
\[ {}4 x y+3 y^{2}-x +x \left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.569 |
|
|
\[ {}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.78 |
|
|
\[ {}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.695 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.128 |
|
|
\[ {}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[_rational] |
✓ |
✓ |
1.726 |
|
|
\[ {}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.742 |
|
|
\[ {}2+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[_rational] |
✓ |
✓ |
1.935 |
|
|
\[ {}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.661 |
|
|
\[ {}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.445 |
|
|
\[ {}x^{2}+y+y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
4.504 |
|
|
\[ {}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.106 |
|
|
\[ {}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.819 |
|
|
\[ {}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0 \] |
1 |
2 |
1 |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
3.208 |
|
|
\[ {}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.677 |
|
|
\[ {}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
32.595 |
|
|
\[ {}2 y^{4} x -y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[_rational] |
❇ |
N/A |
1.056 |
|
|
\[ {}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[_rational] |
❇ |
N/A |
1.203 |
|
|
\[ {}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.072 |
|
|
\[ {}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.551 |
|
|
\[ {}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.938 |
|
|
\[ {}1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.454 |
|
|
\[ {}\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
7 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.683 |
|
|
\[ {}1-\left (y-2 x y\right ) y^{\prime } = 0 \] |
1 |
2 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.245 |
|
|
\[ {}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.132 |
|
|
\[ {}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.215 |
|
|
\[ {}1+\left (x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.112 |
|
|
\[ {}y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime } \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.802 |
|
|
\[ {}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.312 |
|
|
\[ {}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.271 |
|
|
\[ {}y^{\prime } = 1+3 y \tan \left (x \right ) \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.371 |
|
|
\[ {}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.499 |
|
|
\[ {}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.522 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-y = x \left (1+x \right )^{2} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.263 |
|
|
\[ {}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.974 |
|
|
\[ {}y^{\prime }+y^{2} = x^{2}+1 \] |
1 |
1 |
1 |
riccati |
[_Riccati] |
✓ |
✓ |
0.535 |
|
|
\[ {}3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \] |
1 |
3 |
3 |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2} \] |
1 |
1 |
2 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.477 |
|
|
\[ {}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \] |
1 |
2 |
2 |
bernoulli |
[_rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}\left (1+x \right ) \left (y^{\prime }+y^{2}\right )-y = 0 \] |
1 |
1 |
1 |
bernoulli |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.238 |
|
|
\[ {}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0 \] |
1 |
2 |
2 |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.791 |
|
|
\[ {}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0 \] |
1 |
4 |
4 |
bernoulli |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.339 |
|
|
\[ {}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
6 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.864 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \] |
3 |
4 |
4 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.201 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{3} \] |
3 |
3 |
3 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.59 |
|
|
\[ {}x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime } \] |
2 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.622 |
|
|
\[ {}x y^{\prime } \left (y^{\prime }+2\right ) = y \] |
2 |
3 |
3 |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.412 |
|
|
\[ {}x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \] |
4 |
4 |
4 |
quadrature |
[_quadrature] |
✓ |
✓ |
20.843 |
|
|
\[ {}2 {y^{\prime }}^{2} \left (y-x y^{\prime }\right ) = 1 \] |
3 |
4 |
4 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.995 |
|
|
\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \] |
3 |
1 |
7 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
84.592 |
|
|
\[ {}{y^{\prime }}^{3}+y^{2} = x y y^{\prime } \] |
3 |
1 |
3 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
111.411 |
|
|
\[ {}2 x y^{\prime }-y = y^{\prime } \ln \left (y y^{\prime }\right ) \] |
0 |
1 |
4 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.922 |
|
|
\[ {}y = x y^{\prime }-x^{2} {y^{\prime }}^{3} \] |
3 |
1 |
2 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
92.662 |
|
|
\[ {}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2} \] |
3 |
1 |
6 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
103.855 |
|
|
\[ {}x y^{\prime }+y = 4 \sqrt {y^{\prime }} \] |
2 |
3 |
2 |
dAlembert |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
11.989 |
|
|
\[ {}2 x y^{\prime }-y = \ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.606 |
|
|
\[ {}x y^{2} \left (x y^{\prime }+y\right ) = 1 \] |
1 |
1 |
3 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.256 |
|
|
\[ {}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right ) \] |
2 |
2 |
5 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.176 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+x} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.021 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.384 |
|
|
\[ {}1+\sin \left (2 x \right ) y^{2}-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[_exact, _Bernoulli] |
✓ |
✓ |
11.411 |
|
|
\[ {}2 \sqrt {x y}-y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
13.593 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}} \] |
0 |
2 |
1 |
dAlembert, homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.599 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.427 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.437 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.368 |
|
|
\[ {}y^{\prime \prime \prime }+8 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime \prime \prime }-8 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.682 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.776 |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.324 |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
1.32 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.306 |
|
|
\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.372 |
|
|
\[ {}y^{\left (6\right )}-64 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
4.147 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.997 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.297 |
|
|
\[ {}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.947 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.684 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )+x \cos \left (x \right ) \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
2.874 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
13.993 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+{\mathrm e}^{2 x} x \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.353 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.595 |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.136 |
|
|
|
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|
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