|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.339 |
|
|
\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.297 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.371 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.217 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.365 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.346 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.431 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.280 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0
\] |
[_Gegenbauer] |
✓ |
0.379 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.188 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.224 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✓ |
0.264 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.194 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.208 |
|
|
\[
{}x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.227 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
0.360 |
|
|
\[
{}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.286 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.217 |
|
|
\[
{}x y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.237 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.285 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.346 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.286 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.184 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}u^{\prime \prime }+2 u^{\prime }+u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.191 |
|
|
\[
{}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.195 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.184 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.301 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.292 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.294 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.294 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.299 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.297 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.177 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0
\] |
[[_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]] |
✓ |
0.287 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.114 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.198 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.208 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.221 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.131 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.217 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.156 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.177 |
|
|
\[
{}y^{\prime \prime } = \frac {2 y}{x^{2}}
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.162 |
|
|
\[
{}y^{\prime \prime } = \frac {6 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.166 |
|
|
\[
{}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.117 |
|
|
\[
{}y^{\prime \prime } = \frac {20 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime } = \frac {12 y}{x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime }-\frac {y}{4 x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.250 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.299 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.270 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime } = \left (\frac {6}{x^{2}}-1\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime } = \left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.116 |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
108.812 |
|
|
\[
{}y^{\prime \prime } = -\frac {y}{4 x^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.192 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.273 |
|
|
\[
{}x^{2} y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.163 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.193 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.197 |
|
|
\[
{}y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}} = 0
\] |
[_quadrature] |
✓ |
4.320 |
|
|
\[
{}y^{\prime }+a y-c \,{\mathrm e}^{b x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime }+a y-b \sin \left (c x \right ) = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.285 |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
2.263 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x} = 0
\] |
[_linear] |
✓ |
1.903 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-\frac {\sin \left (2 x \right )}{2} = 0
\] |
[_linear] |
✓ |
2.085 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{-\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
1.501 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right )-\sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
1.656 |
|
|
\[
{}y^{\prime }-\left (\sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )+a \right ) y = 0
\] |
[_separable] |
✓ |
1.658 |
|
|
\[
{}y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right ) = 0
\] |
[_linear] |
✓ |
0.565 |
|