|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.487 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.594 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.808 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.485 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (3+x \right ) x y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.466 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.482 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.281 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.343 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.304 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.496 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (3+x \right ) x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.445 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.347 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.453 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.531 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.390 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.461 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.374 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.194 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.441 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.467 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.248 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (-2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.593 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.242 |
|
|
\[
{}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.573 |
|
|
\[
{}x^{4} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.535 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.559 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.337 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 x y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.508 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.362 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.419 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.601 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0
\] |
[_Jacobi] |
✓ |
0.334 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.282 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0
\] |
[_Jacobi] |
✓ |
0.326 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (-2 x +1\right ) y^{\prime }}{3}+\frac {20 y}{9} = 0
\] |
[_Jacobi] |
✓ |
0.354 |
|
|
\[
{}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.289 |
|
|
\[
{}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.489 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.200 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.225 |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.407 |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.489 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.420 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.536 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.180 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.488 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.462 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.458 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.321 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.377 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.402 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.136 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[_Hermite] |
✓ |
0.412 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.401 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
0.365 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.930 |
|
|
\[
{}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.281 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.333 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.256 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.280 |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (y^{\prime } x -y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.264 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.341 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.408 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.304 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.458 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.515 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.548 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
0.368 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.415 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.344 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.604 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.324 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.526 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.326 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.567 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.155 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.273 |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.433 |
|
|
\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.414 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.634 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.279 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.432 |
|