|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.336 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.276 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.285 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.180 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.158 |
|
|
\[
{}u^{\prime \prime }+\frac {u}{x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.277 |
|
|
\[
{}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.190 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.185 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{2 x^{4}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.292 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.287 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.290 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.294 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.292 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.184 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.237 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.285 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.107 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.373 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.268 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.204 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.300 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.203 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.120 |
|
|
\[
{}x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.273 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.204 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.323 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.271 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.288 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.266 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.319 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.205 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.271 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.482 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.228 |
|
|
\[
{}3 y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.314 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.271 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.347 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.276 |
|
|
\[
{}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.477 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.133 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.289 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.210 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.198 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.272 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.295 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.199 |
|
|
\[
{}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.279 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.295 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.279 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.292 |
|
|
\[
{}2 y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.279 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.277 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.075 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.150 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.190 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.373 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.211 |
|
|
\[
{}\left (-2 x +1\right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.287 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.206 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.215 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.156 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.105 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.188 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.181 |
|
|
\[
{}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.211 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.150 |
|
|
\[
{}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.303 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.307 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.134 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.149 |
|