|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.173 |
|
|
\[
{}\left (y-3\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.242 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.394 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.519 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.529 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.462 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.700 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.117 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.361 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 6
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.289 |
|
|
\[
{}2 x y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
0.814 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.351 |
|
|
\[
{}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime } = -y^{\prime } {\mathrm e}^{-y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.495 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.482 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.807 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.760 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.540 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.522 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime } = 4 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.530 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
\] |
[NONE] |
✗ |
0.084 |
|
|
\[
{}3 y+y^{\prime } x = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.078 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.451 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.204 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.141 |
|
|
\[
{}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.368 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.292 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.312 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.309 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.320 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.421 |
|
|
\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.309 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.337 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.302 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.442 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.480 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.360 |
|
|
\[
{}x^{2} y^{\prime \prime }-20 y = 27 x^{5}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.406 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.409 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.064 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.827 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.125 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.937 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.009 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.671 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.513 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.753 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.989 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.711 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.995 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.173 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.094 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.932 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.930 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.282 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.058 |
|
|
\[
{}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.712 |
|
|
\[
{}y^{\prime \prime }-25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.017 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.244 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.803 |
|
|
\[
{}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.806 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.935 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.946 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.219 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.195 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.186 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.800 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.793 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.790 |
|
|
\[
{}25 y^{\prime \prime }-10 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.798 |
|
|
\[
{}16 y^{\prime \prime }-24 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.798 |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.805 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.073 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.070 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.174 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.089 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.090 |
|