|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.300 |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.861 |
|
|
\[
{}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.897 |
|
|
\[
{}2 y x +y^{2}+\left (2 y x +x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.284 |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.250 |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.621 |
|
|
\[
{}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.548 |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
71.793 |
|
|
\[
{}1+\ln \left (y x \right )+\frac {x y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
1.542 |
|
|
\[
{}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.280 |
|
|
\[
{}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
1.091 |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.744 |
|
|
\[
{}y+\left (y^{4}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
13.249 |
|
|
\[
{}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
8.479 |
|
|
\[
{}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.231 |
|
|
\[
{}3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.944 |
|
|
\[
{}2 x \left (1+y\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
0.988 |
|
|
\[
{}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.046 |
|
|
\[
{}4 y x +\left (3 x^{2}+5 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.723 |
|
|
\[
{}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.066 |
|
|
\[
{}y^{\prime } x = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
1.198 |
|
|
\[
{}y^{\prime } x = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
1.898 |
|
|
\[
{}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.405 |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.709 |
|
|
\[
{}x^{2} y^{\prime }-\sqrt {x} = 3
\] |
[_quadrature] |
✓ |
0.300 |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
33.614 |
|
|
\[
{}y^{\prime } = y^{2}-2 y x +x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.365 |
|
|
\[
{}4 y x -6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.252 |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.750 |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
12.957 |
|
|
\[
{}3 y-x^{3}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.224 |
|
|
\[
{}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.491 |
|
|
\[
{}3 x y^{3}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.268 |
|
|
\[
{}2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.373 |
|
|
\[
{}\left (y^{2}-4\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.587 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.339 |
|
|
\[
{}y^{\prime } = \frac {1}{y x -3 x}
\] |
[_separable] |
✓ |
1.278 |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.648 |
|
|
\[
{}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.687 |
|
|
\[
{}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.435 |
|
|
\[
{}\sin \left (x \right )+2 y^{\prime } \cos \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}x y y^{\prime } = 2 x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.845 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{x +2 y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.522 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.567 |
|
|
\[
{}y^{\prime } = x y^{2}+3 y^{2}+x +3
\] |
[_separable] |
✓ |
1.965 |
|
|
\[
{}1-\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.244 |
|
|
\[
{}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.079 |
|
|
\[
{}y^{2}+1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.952 |
|
|
\[
{}x y y^{\prime } = x^{2}+y x +y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.597 |
|
|
\[
{}\left (x +2\right ) y^{\prime }-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.313 |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.099 |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.939 |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.322 |
|
|
\[
{}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.912 |
|
|
\[
{}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}}
\] |
[_Bernoulli] |
✓ |
2.767 |
|
|
\[
{}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
11.333 |
|
|
\[
{}x +y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.395 |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.818 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime }+2 x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.309 |
|
|
\[
{}y^{\prime } = y^{3}-y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.521 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.734 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
1.631 |
|
|
\[
{}y^{\prime } = \tan \left (6 x +3 y+1\right )-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.643 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
1.574 |
|
|
\[
{}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right )
\] |
[_linear] |
✓ |
1.132 |
|
|
\[
{}x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.132 |
|
|
\[
{}x^{2} y^{\prime }+3 y x = 6 \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.187 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.132 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.882 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.073 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.386 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.907 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.733 |
|
|
\[
{}y y^{\prime \prime } = -{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.770 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.306 |
|
|
\[
{}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✗ |
1.655 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.254 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.403 |
|
|
\[
{}\left (y-3\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.187 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.432 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.058 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime \prime \prime } = -2 y^{\prime \prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.348 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.385 |
|
|
\[
{}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.505 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.060 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.792 |
|
|
\[
{}y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.376 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.376 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.710 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.305 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.106 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.250 |
|