|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.339 |
|
|
\[ {}\left (x -1-y^{2}\right ) y^{\prime }-y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
0.852 |
|
|
\[ {}y-\left (x +x y^{3}\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.707 |
|
|
\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \] |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.711 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y-x \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}x y^{\prime } = y+x^{2}+9 y^{2} \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.45 |
|
|
\[ {}x y^{\prime }-3 y = x^{4} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.685 |
|
|
\[ {}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.835 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = \cot \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.515 |
|
|
\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.165 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.387 |
|
|
\[ {}2 y-x^{3} = x y^{\prime } \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.095 |
|
|
\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.646 |
|
|
\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.294 |
|
|
\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.182 |
|
|
\[ {}y^{2} = \left (x^{3}-x y\right ) y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.336 |
|
|
\[ {}x^{2}+y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime } \] |
unknown |
[_rational] |
❇ |
N/A |
1.843 |
|
|
\[ {}x y^{\prime }+y = \cos \left (x \right ) x \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.263 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime } = y^{2} \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}\left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+{\mathrm e}^{x} y = 2 x y^{3} \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}y+x^{2} = x y^{\prime } \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.75 |
|
|
\[ {}x y^{\prime }+y = x^{2} \cos \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.962 |
|
|
\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.287 |
|
|
\[ {}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime } \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
3.343 |
|
|
\[ {}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
32.26 |
|
|
\[ {}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right ) \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
1.388 |
|
|
\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.286 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 4 x^{3} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.955 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
33.056 |
|
|
\[ {}\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime } = 2 x y-{\mathrm e}^{y}-x \] |
exact |
[_exact] |
✓ |
✓ |
1.879 |
|
|
\[ {}{\mathrm e}^{x} \left (1+x \right ) = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.777 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.918 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.664 |
|
|
\[ {}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.897 |
|
|
\[ {}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2} \] |
exact |
[_exact] |
✓ |
✓ |
32.435 |
|
|
\[ {}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
32.579 |
|
|
\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.257 |
|
|
\[ {}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.589 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime } = \cot \left (y\right ) \] |
separable |
[_separable] |
✓ |
✓ |
0.505 |
|
|
\[ {}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \] |
separable |
[_separable] |
✓ |
✓ |
0.743 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \] |
separable |
[_separable] |
✓ |
✓ |
1.624 |
|
|
\[ {}y^{2} y^{\prime } = 2+3 y^{6} \] |
separable |
[_quadrature] |
✓ |
✓ |
1.841 |
|
|
\[ {}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.764 |
|
|
\[ {}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )} \] |
separable |
[_separable] |
✓ |
✓ |
0.517 |
|
|
\[ {}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
1.059 |
|
|
\[ {}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
1.894 |
|
|
\[ {}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.494 |
|
|
\[ {}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.391 |
|
|
\[ {}x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime }+\frac {x}{y}+2 = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.401 |
|
|
\[ {}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.013 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0 \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.566 |
|
|
\[ {}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.218 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.681 |
|
|
\[ {}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.858 |
|
|
\[ {}x^{2}-x y+y^{2}-x y y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.362 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = \frac {2 x +y-1}{x -y-2} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.213 |
|
|
\[ {}y+2 = \left (2 x +y-4\right ) y^{\prime } \] |
homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.103 |
|
|
\[ {}y^{\prime } = \sin \left (x -y\right )^{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.862 |
|
|
\[ {}y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.57 |
|
|
\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
1.747 |
|
|
\[ {}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.895 |
|
|
\[ {}x y^{2}+x -2 y+3+\left (x^{2} y-2 x -2 y\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.205 |
|
|
\[ {}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
32.388 |
|
|
\[ {}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 x y-y \sin \left (2 x \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
33.93 |
|
|
\[ {}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.705 |
|
|
\[ {}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.751 |
|
|
\[ {}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.152 |
|
|
\[ {}4 x y+3 y^{2}-x +x \left (2 y+x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.569 |
|
|
\[ {}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.78 |
|
|
\[ {}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.695 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.128 |
|
|
\[ {}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational] |
✓ |
✓ |
1.726 |
|
|
\[ {}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.742 |
|
|
\[ {}2+y^{2}+2 x +2 y y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational] |
✓ |
✓ |
1.935 |
|
|
\[ {}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.661 |
|
|
\[ {}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.445 |
|
|
\[ {}x^{2}+y+y^{2}-x y^{\prime } = 0 \] |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
4.504 |
|
|
\[ {}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.106 |
|
|
\[ {}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.819 |
|
|
\[ {}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0 \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
3.208 |
|
|
\[ {}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.677 |
|
|
\[ {}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
32.595 |
|
|
\[ {}2 y^{4} x -y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
1.056 |
|
|
\[ {}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
1.203 |
|
|
\[ {}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.072 |
|
|
\[ {}y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.551 |
|
|
\[ {}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.938 |
|
|
\[ {}1+y \cos \left (x \right )-y^{\prime } \sin \left (x \right ) = 0 \] |
linear |
[_linear] |
✓ |
✓ |
0.454 |
|
|
\[ {}\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.683 |
|
|
\[ {}1-\left (y-2 x y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.245 |
|
|
|
||||||
|
|
||||||