|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\ln \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.289 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = x
\] |
[_quadrature] |
✓ |
0.258 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.340 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\] |
[_separable] |
✗ |
2.440 |
|
|
\[
{}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
3.421 |
|
|
\[
{}x^{3} y^{\prime }-\sin \left (y\right ) = 1
\] |
[_separable] |
✓ |
3.668 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\] |
[_separable] |
✓ |
10.291 |
|
|
\[
{}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1
\] |
[_quadrature] |
✓ |
1.326 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = y-1
\] |
[_separable] |
✓ |
1.442 |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
1.160 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
11.876 |
|
|
\[
{}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.607 |
|
|
\[
{}x -y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.246 |
|
|
\[
{}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.139 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.742 |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.293 |
|
|
\[
{}2 x^{2} y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.765 |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.636 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.680 |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.101 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.335 |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.613 |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.474 |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.727 |
|
|
\[
{}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.786 |
|
|
\[
{}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.443 |
|
|
\[
{}x +y+\left (y-1+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.422 |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.784 |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.089 |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.265 |
|
|
\[
{}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.757 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.063 |
|
|
\[
{}x^{2}-x y^{\prime } = y
\] |
[_linear] |
✓ |
1.595 |
|
|
\[
{}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.222 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = 2 x
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}x y^{\prime }-2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.627 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}}
\] |
[_linear] |
✓ |
9.567 |
|
|
\[
{}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.420 |
|
|
\[
{}\left (2 x -y^{2}\right ) y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.944 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[_separable] |
✓ |
1.578 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.444 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.319 |
|
|
\[
{}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.335 |
|
|
\[
{}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.139 |
|
|
\[
{}y^{\prime }-y = -2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.195 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}}
\] |
[_linear] |
✓ |
4.238 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1
\] |
[_linear] |
✓ |
2.385 |
|
|
\[
{}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}}
\] |
[_linear] |
✓ |
1.441 |
|
|
\[
{}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.737 |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
1.877 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.717 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = -\sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.675 |
|
|
\[
{}y^{\prime }+2 x y = 2 x y^{2}
\] |
[_separable] |
✓ |
1.807 |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.266 |
|
|
\[
{}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.213 |
|
|
\[
{}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
1.528 |
|
|
\[
{}y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.810 |
|
|
\[
{}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y}
\] |
[_Bernoulli] |
✓ |
4.466 |
|
|
\[
{}2 \sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
8.836 |
|
|
\[
{}\left (1+x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.285 |
|
|
\[
{}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.361 |
|
|
\[
{}y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.080 |
|
|
\[
{}y^{\prime } \cos \left (y\right )+\sin \left (y\right ) = x +1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.755 |
|
|
\[
{}y y^{\prime }+1 = \left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.714 |
|
|
\[
{}y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.692 |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
260.655 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.688 |
|
|
\[
{}\frac {x}{\sqrt {y^{2}+x^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {y^{2}+x^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
22.773 |
|
|
\[
{}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
45.977 |
|
|
\[
{}2 x +\frac {y^{2}+x^{2}}{x^{2} y} = \frac {\left (y^{2}+x^{2}\right ) y^{\prime }}{x y^{2}}
\] |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
3.559 |
|
|
\[
{}\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
33.559 |
|
|
\[
{}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.369 |
|
|
\[
{}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
18.987 |
|
|
\[
{}\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.066 |
|
|
\[
{}\frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
52.098 |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
10.466 |
|
|
\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\] |
[_exact, _rational] |
✓ |
1.770 |
|
|
\[
{}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
109.534 |
|
|
\[
{}1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.318 |
|
|
\[
{}x^{2}+y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.153 |
|
|
\[
{}x +y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.655 |
|
|
\[
{}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.243 |
|
|
\[
{}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
1.754 |
|
|
\[
{}x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.762 |
|
|
\[
{}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.373 |
|
|
\[
{}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.313 |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.980 |
|
|
\[
{}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.163 |
|
|
\[
{}4 {y^{\prime }}^{2}-9 x = 0
\] |
[_quadrature] |
✓ |
0.264 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left (-1+{\mathrm e}^{2 x}\right )
\] |
[_separable] |
✓ |
0.416 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.481 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
2.954 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_quadrature] |
✓ |
1.163 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
0.847 |
|
|
\[
{}{y^{\prime }}^{3} = y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y
\] |
[_quadrature] |
✓ |
1.193 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.481 |
|