|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.271 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.451 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.244 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.228 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.231 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.243 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.729 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.643 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.949 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.051 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.118 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.998 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.147 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.142 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.131 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = -8
\] |
[[_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)]‘]] |
✓ |
0.863 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.334 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.097 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.658 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.094 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.965 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.623 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.109 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.595 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.366 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.620 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.154 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.156 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.167 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.166 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.170 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.263 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.858 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.516 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.490 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.603 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.426 |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.512 |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.446 |
|
|
\[
{}\left (3 x +2\right ) y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.475 |
|
|
\[
{}\left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.463 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Hermite] |
✓ |
0.325 |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.516 |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.489 |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.420 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.511 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime }+\left (-1+y^{2}\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.370 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.420 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.451 |
|
|
\[
{}y^{\prime \prime }-\cos \left (x \right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.637 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.510 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.157 |
|
|
\[
{}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.514 |
|
|
\[
{}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (5+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.713 |
|
|
\[
{}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.572 |
|
|
\[
{}9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.752 |
|
|
\[
{}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.670 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.410 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.273 |
|
|
\[
{}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.680 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.722 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.738 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.549 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.557 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.289 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.648 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +k \left (k +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.648 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.731 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.569 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.615 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
0.796 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.715 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.445 |
|
|
\[
{}\left (1+t \right )^{2} y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.145 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.347 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.386 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.510 |
|
|
\[
{}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.330 |
|
|
\[
{}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.337 |
|
|
\[
{}20 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.337 |
|
|
\[
{}12 y^{\prime \prime }+8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.355 |
|