|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.713 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.539 |
|
|
\[
{}3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.668 |
|
|
\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.648 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.119 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.731 |
|
|
\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.572 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.211 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.484 |
|
|
\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.612 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.842 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.236 |
|
|
\[
{}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\frac {y}{1-x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.822 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.657 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.148 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.826 |
|
|
\[
{}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
1.209 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.656 |
|
|
\[
{}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.812 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.176 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.757 |
|
|
\[
{}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.951 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.856 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.584 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.031 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.328 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.870 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.191 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.011 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.169 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.961 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.786 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.648 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
1.219 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.313 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.640 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ y^{\prime } t =x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.618 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.626 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.621 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.401 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.524 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.700 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.580 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.590 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.474 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.694 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.634 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.889 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.410 |
|
|
\[
{}y^{\prime } y+y^{4} = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.841 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.176 |
|
|
\[
{}{y^{\prime }}^{2}+y = 0
\] |
[_quadrature] |
✓ |
0.553 |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.506 |
|
|
\[
{}x {y^{\prime \prime }}^{2}+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.115 |
|
|
\[
{}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\] |
[NONE] |
✗ |
0.784 |
|
|
\[
{}2 x -1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.471 |
|
|
\[
{}2 x -y-y^{\prime } y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.737 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.387 |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.593 |
|
|
\[
{}y^{\prime }+y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.091 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.015 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }-10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.348 |
|
|
\[
{}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.617 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+40 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.736 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.102 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.194 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
3.480 |
|
|
\[
{}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.082 |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
2.470 |
|
|
\[
{}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.985 |
|
|
\[
{}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
5.011 |
|
|
\[
{}y^{\prime } = \left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3}
\] |
[_quadrature] |
✓ |
0.538 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_quadrature] |
✓ |
0.246 |
|