|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.588 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.188 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
24.242 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
27.596 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.263 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.114 |
|
|
\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.270 |
|
|
\[
{}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.157 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.904 |
|
|
\[
{}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.552 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.041 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.121 |
|
|
\[
{}\left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
14.196 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.753 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.548 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \left (2-3 y^{\prime } x \right )
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.557 |
|
|
\[
{}x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.794 |
|
|
\[
{}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.710 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.199 |
|
|
\[
{}{y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.377 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
8.936 |
|
|
\[
{}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.787 |
|
|
\[
{}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.586 |
|
|
\[
{}y^{\prime \prime }+y = -\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.280 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.510 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.416 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.356 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.792 |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
2.906 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
79.856 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.625 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.258 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.477 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-y \left (x +1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
5.147 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.956 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.367 |
|
|
\[
{}{y^{\prime }}^{4}+y^{\prime } x -3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.247 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.240 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.749 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.896 |
|
|
\[
{}{y^{\prime }}^{3}-2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.215 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
21.689 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+y^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.639 |
|
|
\[
{}x^{6} {y^{\prime }}^{2} = 16 y+8 y^{\prime } x
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.100 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
3.872 |
|
|
\[
{}\left (1+y^{\prime }\right )^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.856 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.634 |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
3.412 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.748 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.585 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
128.139 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.438 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.665 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.638 |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.648 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.699 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.697 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.680 |
|
|
\[
{}\left (x^{2}-9\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.739 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.512 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x -4 y = 0
\] |
[_Gegenbauer] |
✓ |
0.688 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
1.068 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.671 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.651 |
|
|
\[
{}2 y^{\prime \prime }+9 y^{\prime } x -36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.668 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+3 y^{\prime } x -8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.661 |
|
|
\[
{}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.641 |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.695 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.741 |
|
|
\[
{}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}y^{\prime \prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.547 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.563 |
|
|
\[
{}2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.025 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.990 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.042 |
|
|
\[
{}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.102 |
|
|
\[
{}8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.108 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.899 |
|
|
\[
{}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.898 |
|
|
\[
{}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.131 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.113 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.133 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.126 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.070 |
|