|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.254 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.795 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.847 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.412 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.886 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.810 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.703 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.460 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.785 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +k \left (k +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.704 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.862 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.770 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.765 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
0.883 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.866 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.384 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.743 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.740 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.132 |
|
|
\[
{}\left (1+t \right )^{2} y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.317 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.766 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.796 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.735 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.734 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.520 |
|
|
\[
{}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.745 |
|
|
\[
{}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.750 |
|
|
\[
{}20 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.760 |
|
|
\[
{}12 y^{\prime \prime }+8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.764 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.064 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.928 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 5 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.516 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.657 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.809 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.521 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \frac {1}{{\mathrm e}^{2 t}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.301 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
18.167 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.006 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.092 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.203 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.950 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.419 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.938 |
|
|
\[
{}y^{\prime \prime }-4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.244 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.247 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.413 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.159 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.056 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.031 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.997 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.080 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.685 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.756 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.768 |
|
|
\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.157 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.994 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.000 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.152 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.859 |
|
|
\[
{}5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.745 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.038 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 8 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.670 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.579 |
|
|
\[
{}3 x y^{\prime \prime }+11 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.763 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.699 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0
\] |
[_Jacobi] |
✓ |
0.783 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.796 |
|
|
\[
{}t \left (y^{\prime \prime } y+{y^{\prime }}^{2}\right )+y^{\prime } y = 1
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.562 |
|
|
\[
{}4 x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.963 |
|
|
\[
{}9 x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.801 |
|
|
\[
{}x^{\prime \prime }+64 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.877 |
|
|
\[
{}x^{\prime \prime }+100 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.888 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.673 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.938 |
|
|
\[
{}x^{\prime \prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.799 |
|
|
\[
{}x^{\prime \prime }+256 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.068 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.540 |
|
|
\[
{}10 x^{\prime \prime }+\frac {x}{10} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.881 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.960 |
|
|
\[
{}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.240 |
|
|
\[
{}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.302 |
|
|
\[
{}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.315 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.907 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+20 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.848 |
|