|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime }-13 y^{\prime }+12 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = \cos \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.137 |
|
|
\[
{}y^{\left (6\right )}+y^{\prime \prime \prime \prime } = -24
\] |
[[_high_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \tan \left (t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 3 t^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.194 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \sec \left (t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.638 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sec \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.578 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \cos \left (t \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.779 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = t
\] |
[[_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]] |
✓ |
0.501 |
|
|
\[
{}\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime } = -2-t
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.556 |
|
|
\[
{}2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y = -3 t^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.411 |
|
|
\[
{}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}}
\] |
[[_high_order, _missing_y]] |
✓ |
0.564 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.184 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.204 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.223 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.318 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.909 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.163 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.638 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.039 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.146 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.789 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.156 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.145 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.128 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.133 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.126 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.191 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.693 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.872 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.025 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.849 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.369 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.914 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.275 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.775 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.279 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.277 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.114 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.340 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.942 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.103 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.231 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.227 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 x y^{\prime }-5 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.234 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.235 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.406 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.170 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.415 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.645 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.051 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.343 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.316 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.132 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.236 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.295 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.869 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.657 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.250 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.548 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.634 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
9.090 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.353 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.825 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.750 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.824 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.139 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.145 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.156 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.155 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.150 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.266 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.332 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.655 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.648 |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.318 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.647 |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}\left (2+3 x \right ) y^{\prime \prime }+3 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.597 |
|
|
\[
{}\left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.625 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[_Hermite] |
✓ |
0.534 |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.616 |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.601 |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.499 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.629 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.581 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|