|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.320 |
|
|
\[
{}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.757 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.210 |
|
|
\[
{}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0
\] |
[_Gegenbauer] |
✓ |
0.434 |
|
|
\[
{}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.331 |
|
|
\[
{}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.274 |
|
|
\[
{}z y^{\prime \prime }-2 y^{\prime }+y z = 0
\] |
[_Lienard] |
✓ |
0.353 |
|
|
\[
{}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.181 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.332 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.242 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\] |
[_erf] |
✓ |
0.220 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.344 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0
\] |
[_Gegenbauer] |
✓ |
0.316 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.233 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.374 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.425 |
|
|
\[
{}4 y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[_Lienard] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.304 |
|
|
\[
{}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.507 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.790 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.256 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.370 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.195 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.233 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.237 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.220 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.430 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.243 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.308 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.346 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.422 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.342 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.374 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.217 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.454 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.168 |
|
|
\[
{}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.447 |
|
|
\[
{}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.427 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.344 |
|
|
\[
{}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.464 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.232 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.232 |
|
|
\[
{}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.436 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.350 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.370 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.339 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.524 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0
\] |
[_Jacobi] |
✓ |
0.257 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0
\] |
[_Jacobi] |
✓ |
0.309 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0
\] |
[_Jacobi] |
✓ |
0.318 |
|
|
\[
{}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.215 |
|
|
\[
{}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.367 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.136 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.396 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.433 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.413 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.368 |
|
|
\[
{}\left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.227 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.363 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.165 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.250 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.238 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.239 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.089 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.431 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-3 y = 0
\] |
[_Hermite] |
✓ |
0.246 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[_Hermite] |
✓ |
0.326 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.806 |
|
|
\[
{}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.224 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.309 |
|
|
\[
{}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.178 |
|