|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.224 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.158 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.302 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.094 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.148 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.112 |
|
|
\[
{}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.329 |
|
|
\[
{}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.403 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.037 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.500 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.979 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.773 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.086 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.780 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.371 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.210 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.565 |
|
|
\[
{}y^{\prime \prime }+2 y = 2+{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.829 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.083 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.385 |
|
|
\[
{}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.609 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.787 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
66.873 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.539 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime }+y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.052 |
|
|
\[
{}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.421 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }-y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.315 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.092 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.178 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.482 |
|
|
\[
{}y^{\prime \prime }-y = x \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.448 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.362 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x +x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.874 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.951 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime } = x +\sin \left (\ln \left (x \right )\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.383 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 3 x^{4}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.262 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = \ln \left (x +1\right )^{2}+x -1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.716 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.446 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
1.039 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.613 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.560 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.607 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.122 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.979 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.565 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.365 |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {x +1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
107.729 |
|
|
\[
{}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.898 |
|
|
\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.405 |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.851 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.526 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.303 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.801 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \frac {-x^{2}+1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.719 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.105 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = \frac {2}{x^{3}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.450 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.293 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.533 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.426 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.026 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y = 8
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.062 |
|
|
\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.341 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.336 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.219 |
|
|
\[
{}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x
\] |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
0.079 |
|
|
\[
{}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x}
\] |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.087 |
|
|
\[
{}y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.078 |
|
|
\[
{}2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.258 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }+y=-{\mathrm e}^{t} \\ x+y^{\prime }-y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+y^{\prime }+y=t \\ 5 x+y^{\prime }+3 y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.791 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y^{\prime }+7 y={\mathrm e}^{t}+2 \\ -2 x+y^{\prime }+3 y={\mathrm e}^{t}-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.828 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y^{\prime }+3 y={\mathrm e}^{-t}-1 \\ x^{\prime }+2 x+y^{\prime }+3 y=1+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.223 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y^{\prime }+2 y=1+{\mathrm e}^{t} \\ y^{\prime }+2 y+z^{\prime }+z={\mathrm e}^{t}+2 \\ x^{\prime }-x+z^{\prime }+z=3+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.543 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x^{2}-y
\] |
[_linear] |
✓ |
0.596 |
|
|
\[
{}y^{\prime } x = 1-x +2 y
\] |
[_linear] |
✓ |
0.626 |
|
|
\[
{}y^{\prime } x = 1-x +2 y
\] |
[_linear] |
✓ |
1.682 |
|
|
\[
{}y^{\prime } = 2 x^{2}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.638 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{2}-2 x +y
\] |
[_linear] |
✓ |
0.608 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.526 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.739 |
|