|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.154 |
|
|
\[
{}y^{\prime }+x y = x
\] |
[_separable] |
✓ |
0.354 |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
0.195 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.189 |
|
|
\[
{}2 y-x^{3} = x y^{\prime }
\] |
[_linear] |
✓ |
0.144 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
0.150 |
|
|
\[
{}x y^{\prime }-3 y = x^{4}
\] |
[_linear] |
✓ |
0.138 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
0.180 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
0.204 |
|
|
\[
{}y-x +x y \cot \left (x \right )+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.219 |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.291 |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
0.332 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
[_linear] |
✗ |
0.237 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
0.274 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.306 |
|
|
\[
{}x^{2} y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
0.278 |
|
|
\[
{}x y^{\prime }+y = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.277 |
|
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
53.157 |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.270 |
|
|
\[
{}y^{\prime }+x y = x y^{4}
\] |
[_separable] |
✓ |
2.426 |
|
|
\[
{}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.125 |
|
|
\[
{}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.161 |
|
|
\[
{}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.292 |
|
|
\[
{}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right )
\] |
[_separable] |
✓ |
1.664 |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
2.861 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.378 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
40.201 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.179 |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.443 |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.611 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.606 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
28.066 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
0.270 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.434 |
|
|
\[
{}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
41.481 |
|
|
\[
{}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1
\] |
[_exact, _rational, _Riccati] |
✓ |
1.375 |
|
|
\[
{}2 x y^{4}+\sin \left (y\right )+\left (4 y^{3} x^{2}+x \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.545 |
|
|
\[
{}\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x = 0
\] |
[_exact, _rational, _Riccati] |
✓ |
2.693 |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.754 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.920 |
|
|
\[
{}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
49.583 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
0.445 |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
1.817 |
|
|
\[
{}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.601 |
|
|
\[
{}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.902 |
|
|
\[
{}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.612 |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
70.046 |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.335 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (y^{2}+x^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.376 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.688 |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
15.103 |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.625 |
|
|
\[
{}x y^{\prime } = 2 x -6 y
\] |
[_linear] |
✓ |
1.942 |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.991 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.162 |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.765 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.256 |
|
|
\[
{}2 x -2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.882 |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.070 |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.642 |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.676 |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.278 |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.925 |
|
|
\[
{}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.232 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.187 |
|
|
\[
{}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.138 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.302 |
|
|
\[
{}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.375 |
|
|
\[
{}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.144 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.345 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.363 |
|
|
\[
{}y+\left (x -2 y^{3} x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.326 |
|
|
\[
{}x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.372 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.301 |
|
|
\[
{}y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.345 |
|
|
\[
{}y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.329 |
|
|
\[
{}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
0.334 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.049 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.401 |
|
|
\[
{}x y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
[NONE] |
✗ |
0.095 |
|
|
\[
{}y^{\prime \prime }-k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.302 |
|
|
\[
{}x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.519 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.118 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.247 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.106 |
|
|
\[
{}\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.426 |
|
|
\[
{}y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.552 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.380 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.239 |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_linear] |
✓ |
1.813 |
|
|
\[
{}x^{2} y^{\prime }+y = x^{2}
\] |
[_linear] |
✓ |
0.956 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.348 |
|
|
\[
{}\sec \left (x \right ) y^{\prime } = \sec \left (y\right )
\] |
[_separable] |
✓ |
2.109 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x^{2}}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.237 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.658 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.609 |
|
|
\[
{}-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.483 |
|