|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.073 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}v^{\prime } = g -\frac {k v^{2}}{m}
\] |
[_quadrature] |
✓ |
0.773 |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
71.063 |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.911 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.548 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.033 |
|
|
\[
{}y^{\prime } x = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.878 |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.651 |
|
|
\[
{}y^{\prime } x = 2 x +3 y
\] |
[_linear] |
✓ |
2.455 |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.233 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.691 |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.844 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.716 |
|
|
\[
{}y^{\prime } = \sin \left (x -y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
8.013 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.463 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.722 |
|
|
\[
{}2 x -2 y+\left (-1+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.981 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.465 |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.962 |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.897 |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.490 |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.736 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.641 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
39.923 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.216 |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.141 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.582 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
32.204 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.852 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.836 |
|
|
\[
{}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
41.483 |
|
|
\[
{}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}
\] |
[_exact, _rational, _Riccati] |
✓ |
1.509 |
|
|
\[
{}2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.561 |
|
|
\[
{}\frac {y^{\prime } x +y}{1-x^{2} y^{2}}+x = 0
\] |
[_exact, _rational, _Riccati] |
✓ |
1.747 |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.465 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.704 |
|
|
\[
{}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
53.928 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
5.816 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.544 |
|
|
\[
{}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.461 |
|
|
\[
{}\frac {y-y^{\prime } x}{\left (x +y\right )^{2}}+y^{\prime } = 1
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.840 |
|
|
\[
{}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
55.713 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.181 |
|
|
\[
{}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.153 |
|
|
\[
{}y^{\prime } x +y+3 x^{3} y^{4} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.046 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.360 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.121 |
|
|
\[
{}y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.868 |
|
|
\[
{}x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.219 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.208 |
|
|
\[
{}y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.357 |
|
|
\[
{}y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.336 |
|
|
\[
{}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.939 |
|
|
\[
{}-y+y^{\prime } x = \left (1+y^{2}\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.468 |
|
|
\[
{}y-y^{\prime } x = x y^{3} y^{\prime }
\] |
[_separable] |
✓ |
2.492 |
|
|
\[
{}y^{\prime } x = x^{5}+x^{3} y^{2}+y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.026 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.502 |
|
|
\[
{}y^{\prime } x = y+x^{2}+9 y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.339 |
|
|
\[
{}y^{2}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
2.255 |
|
|
\[
{}-y+y^{\prime } x = 2 x^{2}-3
\] |
[_linear] |
✓ |
1.306 |
|
|
\[
{}y^{\prime } x +y = \sqrt {x y}\, y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
65.276 |
|
|
\[
{}y-x y^{2}+\left (x +x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.230 |
|
|
\[
{}-y+y^{\prime } x = x^{2} y^{4} \left (y^{\prime } x +y\right )
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.462 |
|
|
\[
{}y^{\prime } x +y+x^{2} y^{5} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.165 |
|
|
\[
{}2 x y^{2}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.083 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.307 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.010 |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
1.573 |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
1.595 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
1.618 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.636 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
1.652 |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
1.613 |
|
|
\[
{}y-x +x y \cot \left (x \right )+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.677 |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.365 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
[_linear] |
✓ |
1.372 |
|
|
\[
{}y-2 x y-x^{2}+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}y^{\prime } x +y = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.553 |
|
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
55.157 |
|
|
\[
{}y^{\prime } x +y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.563 |
|
|
\[
{}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.185 |
|
|
\[
{}y-y^{\prime } x = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } x +2 = x^{3} \left (-1+y\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.239 |
|
|
\[
{}y^{\prime } x = 2 x^{2} y+y \ln \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.620 |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
2.927 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.397 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.655 |
|
|
\[
{}y^{\prime \prime }-k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.536 |
|
|
\[
{}x^{2} y^{\prime \prime } = 2 y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.514 |
|
|
\[
{}2 y y^{\prime \prime } = {y^{\prime }}^{2}+1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.082 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.244 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.056 |
|
|
\[
{}\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.367 |
|
|
\[
{}y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.668 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.441 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
6.114 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.253 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.603 |
|