|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.621 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.541 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.149 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
8.461 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
75.258 |
|
|
\[
{}y^{\prime \prime } = y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.404 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.968 |
|
|
\[
{}y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.817 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.052 |
|
|
\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.763 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
94.586 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.164 |
|
|
\[
{}2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
278.162 |
|
|
\[
{}x^{\prime \prime }-k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
12.272 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.385 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.779 |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_separable] |
✓ |
2.608 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.480 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.277 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.451 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.936 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
5.321 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.201 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
1.810 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
1.779 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.965 |
|
|
\[
{}y = x +3 \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
1.731 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.261 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 1
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.940 |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.351 |
|
|
\[
{}2 x^{2} y+{y^{\prime }}^{2} = y^{\prime } x^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.711 |
|
|
\[
{}y {y^{\prime }}^{2} = 3 y^{\prime } x +y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
46.912 |
|
|
\[
{}8 x +1 = y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
3.457 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.211 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.647 |
|
|
\[
{}x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
9.293 |
|
|
\[
{}y+2 y^{\prime } x = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.668 |
|
|
\[
{}x = {y^{\prime }}^{2}+y^{\prime }
\] |
[_quadrature] |
✓ |
0.112 |
|
|
\[
{}x = y-{y^{\prime }}^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.267 |
|
|
\[
{}x +2 y y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.755 |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.476 |
|
|
\[
{}x {y^{\prime }}^{3} = y y^{\prime }+1
\] |
[_dAlembert] |
✓ |
0.141 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.586 |
|
|
\[
{}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.799 |
|
|
\[
{}x = y y^{\prime }+{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
3.727 |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 y^{\prime } x = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.592 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.414 |
|
|
\[
{}2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.391 |
|
|
\[
{}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.430 |
|
|
\[
{}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.679 |
|
|
\[
{}2 {y^{\prime }}^{5}+2 y^{\prime } x = y
\] |
[_dAlembert] |
✓ |
0.538 |
|
|
\[
{}\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x = 2 y
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
27.344 |
|
|
\[
{}2 y = 3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
6.281 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.249 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.829 |
|
|
\[
{}y = y^{\prime } x -\sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.865 |
|
|
\[
{}y = y^{\prime } x +\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.849 |
|
|
\[
{}y = y^{\prime } x +\frac {3}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.919 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{{2}/{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.346 |
|
|
\[
{}y = y^{\prime } x +{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.409 |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.918 |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.260 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
3.836 |
|
|
\[
{}y^{\prime } = \sqrt {1-y}
\] |
[_quadrature] |
✓ |
0.080 |
|
|
\[
{}y^{\prime } = y x -x^{2}
\] |
[_linear] |
✓ |
0.191 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
0.099 |
|
|
\[
{}y^{\prime } = 3 x +\frac {y}{x}
\] |
[_linear] |
✓ |
0.696 |
|
|
\[
{}y^{\prime } = \ln \left (y x \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.173 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.079 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime } = \sqrt {y x +1}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.628 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.262 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime } = \sin \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime } = \sin \left (y x \right )
\] |
[NONE] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime } = \cos \left (y x \right )
\] |
[NONE] |
✓ |
0.549 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.938 |
|
|
\[
{}3 x \left (2+3 x \right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.664 |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.498 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.087 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.543 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.157 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.582 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.131 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.639 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.273 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.592 |
|
|
\[
{}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.602 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.083 |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.562 |
|
|
\[
{}\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|