|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.149 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.152 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.253 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.194 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.624 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.624 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.699 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.704 |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.586 |
|
|
\[
{}\left (2+3 x \right ) y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.556 |
|
|
\[
{}\left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.585 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.638 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Hermite] |
✓ |
0.526 |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.586 |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.521 |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.452 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.621 |
|
|
\[
{}y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.473 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.552 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime }-y \cos \left (x \right ) = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.671 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.572 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.124 |
|
|
\[
{}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.690 |
|
|
\[
{}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.786 |
|
|
\[
{}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.689 |
|
|
\[
{}9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.811 |
|
|
\[
{}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_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]] |
✓ |
1.163 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.806 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.857 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.801 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.670 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.675 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.443 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.777 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +k \left (k +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.707 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.836 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.716 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.798 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_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]] |
✓ |
0.789 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.078 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.068 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.496 |
|
|
\[
{}\left (1+t \right )^{2} y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.308 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.371 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.072 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.161 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.032 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.049 |
|
|
\[
{}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.073 |
|
|
\[
{}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.079 |
|
|
\[
{}20 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.085 |
|
|
\[
{}12 y^{\prime \prime }+8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.086 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 5 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.253 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.475 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.060 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.365 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \frac {1}{1+{\mathrm e}^{2 t}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.135 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.309 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.009 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.668 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.893 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.393 |
|
|
\[
{}y^{\prime \prime }-4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.287 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.080 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.072 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.873 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.426 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.414 |
|