|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{2} \left ({y^{\prime }}^{2}+1\right ) = a^{2}
\] |
[_quadrature] |
✓ |
4.460 |
|
|
\[
{}y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.542 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.601 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.436 |
|
|
\[
{}y = {y^{\prime }}^{2} \left (x +1\right )
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.717 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime }
\] |
[_rational] |
✓ |
117.895 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.081 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.553 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
3.414 |
|
|
\[
{}y = y^{\prime } x +\frac {y {y^{\prime }}^{2}}{x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.074 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = x^{2} y^{2}+x^{4}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.378 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.362 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.328 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.559 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2} = 0
\] |
[_quadrature] |
✓ |
1.002 |
|
|
\[
{}8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
30.420 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.251 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
11.697 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.074 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.046 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.064 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.326 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.240 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.932 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.852 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.131 |
|
|
\[
{}y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.599 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.802 |
|
|
\[
{}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.411 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.931 |
|
|
\[
{}y^{\prime \prime \prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime } = 3 x^{2}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = {\mathrm e}^{x}+4
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.185 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.012 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = x \ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.256 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.750 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.846 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
16.716 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.046 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.538 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x^{2}-3 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.138 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \left (1+\ln \left (x \right )\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.832 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{2}-x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.413 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.793 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.621 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime \prime }-y = x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.022 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.678 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = x^{2}-x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.664 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.587 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y = {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.911 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.599 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.619 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.829 |
|
|
\[
{}y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.897 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.422 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.328 |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.524 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.569 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
0.940 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.160 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.254 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.152 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.480 |
|
|
\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.589 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.730 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.116 |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.789 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.728 |
|
|
\[
{}\left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2} = {y^{\prime \prime \prime }}^{2}+1
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.002 |
|
|
\[
{}\left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.770 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.408 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.151 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
32.757 |
|
|
\[
{}y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.278 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.062 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime } x +y = -x^{2}+1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.061 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime } = 1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.485 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.697 |
|