|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.142 |
|
|
\[
{}\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.732 |
|
|
\[
{}2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.548 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.106 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.104 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t}
\] |
[[_high_order, _missing_y]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.841 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.168 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \tan \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right ) \tan \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.636 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \sec \left (2 t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.641 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \tan \left (2 t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.656 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \sec \left (3 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = -\sec \left (t \right ) \tan \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = -\frac {1}{t^{2}}-\frac {2}{t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }-13 y^{\prime }+12 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = \cos \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.129 |
|
|
\[
{}y^{\left (6\right )}+y^{\prime \prime \prime \prime } = -24
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \tan \left (t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 3 t^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \sec \left (t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sec \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.540 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \cos \left (t \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.763 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = t
\] |
[[_high_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.400 |
|
|
\[
{}\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime } = -2-t
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.503 |
|
|
\[
{}2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y = -3 t^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.386 |
|
|
\[
{}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}}
\] |
[[_high_order, _missing_y]] |
✓ |
0.234 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.113 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.139 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.163 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.251 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.831 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.010 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.562 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.940 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.095 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.715 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.091 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.091 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.131 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.126 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.126 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.257 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \frac {1}{x^{5}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.586 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.754 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.876 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.734 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.298 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.800 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.150 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +36 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.633 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y = \frac {1}{x^{3}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.264 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y = \frac {1}{x^{13}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.269 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.994 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.327 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.817 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.005 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.235 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.233 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.220 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.985 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.314 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.330 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.960 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.290 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.214 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.117 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = -8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.221 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.204 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.835 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.487 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.078 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.420 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.564 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
8.783 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.282 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.651 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.649 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.692 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|