|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
41.779 |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.674 |
|
|
\[
{}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.364 |
|
|
\[
{}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.375 |
|
|
\[
{}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.622 |
|
|
\[
{}x y^{\prime } = 2 x^{2} y+y \ln \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.858 |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
3.618 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.163 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }-k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.887 |
|
|
\[
{}x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.472 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.075 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.333 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.015 |
|
|
\[
{}\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
3.611 |
|
|
\[
{}y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.926 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.555 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.694 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.268 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.827 |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.517 |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.830 |
|
|
\[
{}y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.822 |
|
|
\[
{}x^{2} y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.132 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.080 |
|
|
\[
{}x y^{\prime }+y = x^{2} y^{\prime }+y^{2}
\] |
[_separable] |
✓ |
2.729 |
|
|
\[
{}x y y^{\prime } = x^{2} y^{\prime }+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
73.605 |
|
|
\[
{}\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.175 |
|
|
\[
{}y^{\prime \prime }+2 x {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.223 |
|
|
\[
{}x^{2}+y = x y^{\prime }
\] |
[_linear] |
✓ |
1.660 |
|
|
\[
{}x y^{\prime }+y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.552 |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.968 |
|
|
\[
{}\cos \left (x +y\right ) = x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
4.826 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.821 |
|
|
\[
{}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
35.752 |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
2.214 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.725 |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
80.409 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
1.810 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{x} \cos \left (y\right ) y^{\prime } = y \sin \left (x y\right )+x \sin \left (x y\right ) y^{\prime }
\] |
[_exact] |
✓ |
40.325 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.780 |
|
|
\[
{}\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\] |
[NONE] |
✗ |
0.212 |
|
|
\[
{}\left (x +1\right ) {\mathrm e}^{x} = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.939 |
|
|
\[
{}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.251 |
|
|
\[
{}y^{\prime } = 1+3 \tan \left (x \right ) y
\] |
[_linear] |
✓ |
1.577 |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.995 |
|
|
\[
{}y^{\prime } = \frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
71.808 |
|
|
\[
{}y^{\prime } = \frac {x +2 y+2}{-2 x +y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.569 |
|
|
\[
{}3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
2.262 |
|
|
\[
{}\frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
38.766 |
|
|
\[
{}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0
\] |
[_linear] |
✓ |
4.513 |
|
|
\[
{}x y^{2}+y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.617 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.427 |
|
|
\[
{}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
8.557 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+2 y = \left (x^{2}+1\right )^{3}
\] |
[_linear] |
✓ |
1.540 |
|
|
\[
{}y^{\prime } = \frac {-3 x -2 y-1}{2 x +3 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.295 |
|
|
\[
{}{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.369 |
|
|
\[
{}3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.508 |
|
|
\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.374 |
|
|
\[
{}3 x y+y^{2}+\left (3 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
70.917 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.546 |
|
|
\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.559 |
|
|
\[
{}\frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
38.746 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.201 |
|
|
\[
{}x y+y-1+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.207 |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.981 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.304 |
|
|
\[
{}x^{\prime }+x \cot \left (y \right ) = \sec \left (y \right )
\] |
[_linear] |
✓ |
1.911 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.979 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.743 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.049 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.046 |
|
|
\[
{}y^{\prime \prime }-2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.582 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.777 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.064 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.418 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.224 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.994 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.981 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.365 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.061 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.880 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.163 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.967 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.169 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.515 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.287 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.248 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.078 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.086 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.104 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{-1+x}+\frac {y}{-1+x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.100 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.082 |
|