|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.630 |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+y^{\prime } x = 0
\] |
[_Bernoulli] |
✓ |
2.216 |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_linear] |
✓ |
2.505 |
|
|
\[
{}y^{\prime } = \frac {1}{2 x -y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.002 |
|
|
\[
{}x^{2}+y^{\prime } x = 3 x +y^{\prime }
\] |
[_quadrature] |
✓ |
0.396 |
|
|
\[
{}x y^{\prime } y-y^{2} = x^{4}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.161 |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.201 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}}
\] |
[_linear] |
✓ |
1.039 |
|
|
\[
{}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.368 |
|
|
\[
{}y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right ) = \cos \left (\frac {x}{2}-\frac {y}{2}\right )
\] |
[_separable] |
✓ |
4.979 |
|
|
\[
{}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0
\] |
[_separable] |
✓ |
1.158 |
|
|
\[
{}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.676 |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
5.042 |
|
|
\[
{}x^{2}+y^{2}-x y^{\prime } y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.350 |
|
|
\[
{}x -y+2+\left (x -y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.815 |
|
|
\[
{}y+x y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.764 |
|
|
\[
{}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.316 |
|
|
\[
{}\left (x -1\right ) \left (y^{2}-y+1\right ) = \left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.229 |
|
|
\[
{}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.942 |
|
|
\[
{}\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.232 |
|
|
\[
{}y^{\prime }-1 = {\mathrm e}^{x +2 y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.275 |
|
|
\[
{}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.590 |
|
|
\[
{}x^{2} y^{n} y^{\prime } = 2 y^{\prime } x -y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.839 |
|
|
\[
{}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.003 |
|
|
\[
{}x -y^{2}+2 x y^{\prime } y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.051 |
|
|
\[
{}y^{\prime } x +y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.570 |
|
|
\[
{}\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.552 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.299 |
|
|
\[
{}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.609 |
|
|
\[
{}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.073 |
|
|
\[
{}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.055 |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
1.861 |
|
|
\[
{}4 x^{2} {y^{\prime }}^{2}-y^{2} = x y^{3}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.454 |
|
|
\[
{}y^{\prime }+x {y^{\prime }}^{2}-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.154 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )+2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.886 |
|
|
\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.505 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.725 |
|
|
\[
{}{y^{\prime }}^{4} = 1
\] |
[_quadrature] |
✓ |
0.508 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.267 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.425 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.612 |
|
|
\[
{}y^{\prime \prime \prime \prime } = x
\] |
[[_high_order, _quadrature]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime } = x +\cos \left (x \right )
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime } \left (x +2\right )^{5} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.725 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.324 |
|
|
\[
{}y^{\prime \prime } = 2 x \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.030 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.000 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.827 |
|
|
\[
{}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.819 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.941 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.536 |
|
|
\[
{}x y = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[_separable] |
✓ |
2.619 |
|
|
\[
{}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
527.245 |
|
|
\[
{}y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
4.847 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.207 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.559 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.544 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.708 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.540 |
|
|
\[
{}y^{\prime \prime } = \sqrt {y^{\prime }+1}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.617 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }+1\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.194 |
|
|
\[
{}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.900 |
|
|
\[
{}y^{\prime \prime \prime }+{y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.646 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
15.761 |
|
|
\[
{}3 y^{\prime } y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
3.446 |
|
|
\[
{}2 y^{\prime \prime } = 3 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
3.495 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.248 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.523 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.694 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.389 |
|
|
\[
{}y^{3} y^{\prime \prime } = -1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.300 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.741 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.603 |
|
|
\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.681 |
|
|
\[
{}y^{\prime \prime \prime } = 3 y y^{\prime }
\] |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.082 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.374 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.591 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.422 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.453 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.728 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\left (5\right )} = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.086 |
|