|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.373 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.879 |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.470 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.869 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.804 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.571 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
2.055 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.484 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.526 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.588 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.684 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.598 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.775 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.594 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}x^{\prime \prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.732 |
|
|
\[
{}x^{\prime \prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.082 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.933 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.914 |
|
|
\[
{}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.000 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.233 |
|
|
\[
{}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.667 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.994 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.669 |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
[_quadrature] |
✓ |
1.857 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
1.557 |
|
|
\[
{}y^{\prime }-2 \sqrt {{| y|}} = 0
\] |
[_quadrature] |
✓ |
2.973 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
2.262 |
|
|
\[
{}y^{\prime }-y^{2} = 1
\] |
[_quadrature] |
✓ |
3.381 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.934 |
|
|
\[
{}x y^{\prime }-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.584 |
|
|
\[
{}y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
1.753 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.880 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.050 |
|
|
\[
{}2 x y^{\prime }-y = 0
\] |
[_separable] |
✓ |
2.242 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.514 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.189 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.879 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}{y^{\prime }}^{2}-9 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.654 |
|
|
\[
{}{y^{\prime }}^{2} = x^{6}
\] |
[_quadrature] |
✓ |
0.558 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
1.652 |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.354 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.838 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
4.438 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.050 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
2.115 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
1.821 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.370 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.967 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.961 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.752 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.833 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.733 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.760 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.272 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.989 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.449 |
|
|
\[
{}y^{\prime } = -1+x
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.427 |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
1.386 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
3.904 |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
[_quadrature] |
✓ |
3.749 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.645 |
|
|
\[
{}y^{\prime } = -x y
\] |
[_separable] |
✓ |
1.687 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.173 |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.287 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.661 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
4.490 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.683 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
3.300 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
2.017 |
|
|
\[
{}y^{\prime } = x^{3}+y^{3}
\] |
[_Abel] |
✗ |
0.757 |
|
|
\[
{}y^{\prime } = {| y|}
\] |
[_quadrature] |
✓ |
1.481 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.422 |
|
|
\[
{}y^{\prime } = \ln \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.386 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.530 |
|
|
\[
{}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.224 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.597 |
|
|
\[
{}y^{\prime } = \frac {1}{x y}
\] |
[_separable] |
✓ |
2.480 |
|
|
\[
{}y^{\prime } = \ln \left (y-1\right )
\] |
[_quadrature] |
✓ |
1.332 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
54.013 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.275 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.495 |
|