|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime \prime \prime } = -2 y^{\prime \prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.392 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.429 |
|
|
\[
{}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.536 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.198 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.774 |
|
|
\[
{}y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.406 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.902 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.327 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.190 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.274 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.198 |
|
|
\[
{}\left (-3+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.551 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.549 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.697 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.621 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.838 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.144 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.389 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 6
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.531 |
|
|
\[
{}2 x y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
0.533 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.401 |
|
|
\[
{}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y^{\prime } y
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.459 |
|
|
\[
{}y^{\prime \prime } = -y^{\prime } {\mathrm e}^{-y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.959 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.734 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.853 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.631 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.640 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime } = 4 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.634 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
\] |
[NONE] |
✗ |
0.088 |
|
|
\[
{}x y^{\prime }+3 y = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.136 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
10.987 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.146 |
|
|
\[
{}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.403 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.395 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.312 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.333 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.301 |
|
|
\[
{}y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.451 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.339 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1+\cos \left (x \right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.393 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.322 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.475 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.383 |
|
|
\[
{}x^{2} y^{\prime \prime }-20 y = 27 x^{5}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.400 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.437 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.432 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.142 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.562 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.428 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.175 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.974 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.754 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.098 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.304 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.036 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.182 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.567 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.403 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.064 |
|
|
\[
{}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.837 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.821 |
|
|
\[
{}y^{\prime \prime }-25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.144 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.386 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.889 |
|
|
\[
{}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.842 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.396 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.406 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.422 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.627 |
|