|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
262.393 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.293 |
|
|
\[
{}y = y^{\prime } x +k {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.328 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.240 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.199 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.456 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.927 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.495 |
|
|
\[
{}y^{\prime } \left (y^{\prime } x -y+k \right )+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.469 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
12.093 |
|
|
\[
{}y = x^{6} {y^{\prime }}^{3}-y^{\prime } x
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
14.033 |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.713 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.569 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.365 |
|
|
\[
{}2 {y^{\prime }}^{3}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.464 |
|
|
\[
{}2 {y^{\prime }}^{2}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.477 |
|
|
\[
{}{y^{\prime }}^{3}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.484 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.448 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.466 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.416 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.087 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.376 |
|
|
\[
{}{y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.359 |
|
|
\[
{}y = y^{\prime } x +x^{3} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.931 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.423 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.544 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.563 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.367 |
|
|
\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.319 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.233 |
|
|
\[
{}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.374 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.373 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.519 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.244 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.622 |
|
|
\[
{}y^{\prime \prime }+\beta ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.538 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.489 |
|
|
\[
{}y^{\prime \prime } \cos \left (x \right ) = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.148 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
21.988 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
25.065 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.749 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.781 |
|
|
\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.952 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.183 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.213 |
|
|
\[
{}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.993 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.195 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.486 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.032 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.101 |
|
|
\[
{}\left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
12.990 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.670 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.419 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \left (2-3 y^{\prime } x \right )
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.528 |
|
|
\[
{}x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.709 |
|
|
\[
{}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.652 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
4.924 |
|
|
\[
{}{y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.335 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
9.536 |
|
|
\[
{}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.620 |
|
|
\[
{}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.493 |
|
|
\[
{}y^{\prime \prime }+y = -\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.207 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.033 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.135 |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.838 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
176.945 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.638 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.211 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.380 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-y \left (x +1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
2.916 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
7.010 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
204.875 |
|
|
\[
{}{y^{\prime }}^{4}+y^{\prime } x -3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.048 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.171 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.857 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.441 |
|
|
\[
{}{y^{\prime }}^{3}-2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.183 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
18.187 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+y^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.584 |
|
|
\[
{}x^{6} {y^{\prime }}^{2} = 16 y+8 y^{\prime } x
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.169 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
2.605 |
|
|
\[
{}\left (y^{\prime }+1\right )^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.816 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.646 |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
1.835 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.817 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.538 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
227.768 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.318 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.525 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.587 |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.606 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.615 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.479 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|