|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.184 |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.588 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.237 |
|
|
\[
{}2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.193 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.220 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.363 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.309 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.237 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.316 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.445 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.437 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[_Hermite] |
✓ |
0.328 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.310 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.460 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.448 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.232 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.431 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.300 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.091 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.172 |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.329 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.393 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.359 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.361 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.417 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.255 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.307 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.089 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0
\] |
[_Gegenbauer] |
✓ |
0.381 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.156 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.181 |
|
|
\[
{}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✓ |
0.217 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.171 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.097 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.180 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.179 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
0.352 |
|
|
\[
{}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.341 |
|
|
\[
{}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.363 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.226 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.191 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.184 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.243 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.367 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.300 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.247 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.126 |
|
|
\[
{}u^{\prime \prime }+2 u^{\prime }+u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.162 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.321 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.324 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.154 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.202 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.210 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.392 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.233 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.162 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.172 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.172 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.173 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime } = \frac {2 y}{x^{2}}
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime } = \frac {6 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.132 |
|
|
\[
{}y^{\prime \prime } = \frac {20 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime } = \frac {12 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime }-\frac {y}{4 x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.227 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.323 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.769 |
|