|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime }+P \left (x \right ) y = Q \left (x \right )
\] |
[_linear] |
✓ |
2.034 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.803 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.310 |
|
|
\[
{}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.159 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.682 |
|
|
\[
{}y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.830 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.869 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.722 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.249 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = \sin \left (x \right )-{\mathrm e}^{4 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.834 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.757 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.000 |
|
|
\[
{}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.787 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.700 |
|
|
\[
{}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.710 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.392 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.718 |
|
|
\[
{}y^{\prime \prime \prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
3.941 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.245 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x^{2} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2}+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.168 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{3}-\frac {\cos \left (2 x \right )}{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.695 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2} \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.239 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.684 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.409 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.718 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.180 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.698 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = x \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.236 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.592 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.751 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.498 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
4.376 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.438 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.352 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
6.833 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.040 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.818 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.263 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.398 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.846 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = \ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.786 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.803 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 1-x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
6.128 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.270 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.890 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.125 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y = \left (x -1\right ) \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.432 |
|
|
\[
{}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y = x +\ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.323 |
|
|
\[
{}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y = \frac {4}{x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.498 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y = \cos \left (\ln \left (x \right )\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
7.879 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-y^{\prime } x +4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.028 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x=\cos \left (t \right ) \\ y^{\prime }+y=4 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x=3 t^{2} \\ y^{\prime }+y={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.393 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x=3 t \\ x^{\prime }+2 y^{\prime }+y=\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.741 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \\ x^{\prime }+y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.671 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+3 x-y={\mathrm e}^{t} \\ 5 x-3 y^{\prime }=y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.652 |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }-3 x^{\prime }-5 y=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=2 x+3 y \\ z^{\prime }=3 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.445 |
|
|
\[
{}y^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.447 |
|
|
\[
{}y^{\prime \prime } = k^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.935 |
|
|
\[
{}x^{\prime \prime }+k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.722 |
|
|
\[
{}y^{3} y^{\prime \prime }+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.268 |
|
|
\[
{}x^{\prime \prime } = \frac {k^{2}}{x^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
75.647 |
|
|
\[
{}x y^{\prime \prime } = x^{2}+1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.970 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.131 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.967 |
|
|
\[
{}x y^{\prime \prime }+x = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.149 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime } = t^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.312 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.693 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.631 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
41.918 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.691 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.955 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
5.267 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.493 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.226 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.558 |
|
|
\[
{}y y^{\prime \prime }+1 = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
13.224 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.735 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.050 |
|