|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.069 |
|
|
\[
{}y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.105 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.497 |
|
|
\[
{}y^{\prime \prime }+y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.529 |
|
|
\[
{}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.208 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.489 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.718 |
|
|
\[
{}x^{3} x^{\prime \prime }+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.119 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.136 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
5.966 |
|
|
\[
{}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.441 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.191 |
|
|
\[
{}y^{\prime \prime } = 3 \sqrt {y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.146 |
|
|
\[
{}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.877 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.672 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.367 |
|
|
\[
{}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.505 |
|
|
\[
{}x^{\prime \prime }+9 x = t \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.996 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.682 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.670 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.123 |
|
|
\[
{}m x^{\prime \prime } = f \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.110 |
|
|
\[
{}m x^{\prime \prime } = f \left (x^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.535 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.128 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.996 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.552 |
|
|
\[
{}x^{3} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.319 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = t^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.127 |
|
|
\[
{}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.200 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.783 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.256 |
|
|
\[
{}y^{\left (6\right )}-y = {\mathrm e}^{2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.151 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
0.454 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.665 |
|
|
\[
{}y^{\prime \prime } = 2 y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.304 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.268 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x-3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.852 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.759 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right )
\] |
[_separable] |
✓ |
1.618 |
|
|
\[
{}x^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.940 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.362 |
|
|
\[
{}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime }
\] |
[_separable] |
✓ |
2.066 |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.549 |
|
|
\[
{}y^{\prime } x +y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.480 |
|
|
\[
{}y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.638 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y^{2}-x}
\] |
[_separable] |
✓ |
1.347 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.637 |
|
|
\[
{}x \left (1+y\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }
\] |
[_separable] |
✓ |
2.347 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.823 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.060 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
5.468 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3
\] |
[[_high_order, _missing_y]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.059 |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
[_linear] |
✓ |
38.730 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.061 |
|
|
\[
{}y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.712 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.400 |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
1.575 |
|
|
\[
{}{y^{\prime }}^{2} \sqrt {y} = \sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.089 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.543 |
|
|
\[
{}y^{\prime \prime \prime } = 1
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.089 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.352 |
|
|
\[
{}y^{\prime \prime } = y+x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.064 |
|
|
\[
{}{y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.543 |
|
|
\[
{}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.057 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\] |
[NONE] |
✗ |
0.223 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.505 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.059 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.375 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.117 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.089 |
|
|
\[
{}3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.299 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.191 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.022 |
|
|
\[
{}x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right ) = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.194 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.498 |
|
|
\[
{}y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.796 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.201 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.579 |
|
|
\[
{}y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.134 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.057 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.856 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.522 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.813 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.598 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.489 |
|
|
\[
{}\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.810 |
|