|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{-t^{2}} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.863 |
|
|
\[
{}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.284 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.843 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.895 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.832 |
|
|
\[
{}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.878 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.874 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.855 |
|
|
\[
{}4 y^{\prime \prime }+17 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.880 |
|
|
\[
{}16 y^{\prime \prime }+24 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.945 |
|
|
\[
{}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.914 |
|
|
\[
{}2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.558 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.228 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.149 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+82 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.730 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.240 |
|
|
\[
{}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.229 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+\frac {y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.946 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.323 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.392 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.320 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.396 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.399 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.215 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.174 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.309 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.412 |
|
|
\[
{}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.168 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.720 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.051 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.069 |
|
|
\[
{}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.081 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.164 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \csc \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.433 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.154 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.744 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime }+4 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.986 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.128 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.636 |
|
|
\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.300 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.691 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.821 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.733 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.107 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.785 |
|
|
\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.315 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right ) {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.816 |
|
|
\[
{}u^{\prime \prime }+2 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.002 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.738 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.598 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.547 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.958 |
|
|
\[
{}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\] |
[NONE] |
✗ |
0.099 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.490 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.627 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.558 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.500 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.586 |
|
|
\[
{}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.608 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.507 |
|
|
\[
{}2 y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.538 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.516 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.629 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.518 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.514 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.623 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.514 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.474 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.547 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.515 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.857 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.673 |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.669 |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.732 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.667 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.799 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.633 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.678 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.504 |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.558 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
0.569 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (1+\alpha \right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.735 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }=\frac {x_{1}}{10}-\frac {x_{2}}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|