|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+\cos \left (y\right ) = 0
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.535 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
0.675 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.536 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.706 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
52.899 |
|
|
\[
{}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.342 |
|
|
\[
{}y^{\prime \prime }+\frac {\left ({\mathrm e}^{x}+1\right ) y}{1-{\mathrm e}^{x}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.393 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.461 |
|
|
\[
{}x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.679 |
|
|
\[
{}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.066 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.564 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[_separable] |
✓ |
0.543 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.571 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.569 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.620 |
|
|
\[
{}y^{\prime \prime }+3 x y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.674 |
|
|
\[
{}x y^{\prime \prime }-3 x y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime }+y \ln \left (x \right ) = 0
\] |
[_Titchmarsh] |
✓ |
0.572 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.702 |
|
|
\[
{}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.805 |
|
|
\[
{}y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.907 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.162 |
|
|
\[
{}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.860 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.636 |
|
|
\[
{}y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.852 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.858 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.750 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.358 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.537 |
|
|
\[
{}\left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.448 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.381 |
|
|
\[
{}3 \left (-2+x \right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.510 |
|
|
\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.455 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{-2+x}+\frac {2 y}{x +2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.026 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.586 |
|
|
\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.259 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.036 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.703 |
|
|
\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.702 |
|
|
\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.402 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.343 |
|
|
\[
{}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.733 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.453 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.253 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.727 |
|
|
\[
{}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.780 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
1.419 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.725 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.471 |
|
|
\[
{}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.645 |
|
|
\[
{}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (-1+x \right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.722 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.766 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.679 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.446 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.870 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.706 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.528 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.737 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.358 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.858 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.828 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.351 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.829 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.694 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.446 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
1.444 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.452 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.684 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ t y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.032 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.634 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.637 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.635 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.556 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.542 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.784 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.600 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.683 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.774 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.766 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.037 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.481 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|