|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime } = \left (-2 x^{2}+1\right ) \tan \left (y\right )
\] |
[_separable] |
✓ |
2.083 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.641 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.559 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.668 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.805 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.828 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
2.325 |
|
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
[_separable] |
✓ |
2.084 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.746 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.833 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.462 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.702 |
|
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.805 |
|
|
\[
{}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
[_quadrature] |
✓ |
1.353 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}
\] |
[_separable] |
✓ |
5.398 |
|
|
\[
{}x y^{\prime } = 2 x^{2}+1
\] |
[_quadrature] |
✓ |
0.769 |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.811 |
|
|
\[
{}3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.362 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.929 |
|
|
\[
{}x y y^{\prime } = \left (x +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
2.016 |
|
|
\[
{}y^{\prime } = 2 x y+1
\] |
[_linear] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.869 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}v^{\prime } = g -\frac {k v^{2}}{m}
\] |
[_quadrature] |
✓ |
2.484 |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
64.003 |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.257 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.258 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.595 |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
41.352 |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.453 |
|
|
\[
{}x y^{\prime } = 2 x +3 y
\] |
[_linear] |
✓ |
2.672 |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.712 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.015 |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.683 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.542 |
|
|
\[
{}y^{\prime } = \sin \left (x -y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.431 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.549 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.781 |
|
|
\[
{}2 x -2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.335 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.859 |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
2.046 |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.420 |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.984 |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.881 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.654 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
41.892 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.325 |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.275 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.646 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
31.757 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.748 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.799 |
|
|
\[
{}2 x y^{3}+y \cos \left (x \right )+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
41.727 |
|
|
\[
{}1 = \frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}}
\] |
[_exact, _rational, _Riccati] |
✓ |
1.731 |
|
|
\[
{}2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.388 |
|
|
\[
{}\frac {x y^{\prime }+y}{1-y^{2} x^{2}}+x = 0
\] |
[_exact, _rational, _Riccati] |
✓ |
1.733 |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.655 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.117 |
|
|
\[
{}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
67.142 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
6.970 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.309 |
|
|
\[
{}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.809 |
|
|
\[
{}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.095 |
|
|
\[
{}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
53.187 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
36.500 |
|
|
\[
{}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.345 |
|
|
\[
{}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
12.049 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.461 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.761 |
|
|
\[
{}y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
196.270 |
|
|
\[
{}x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.432 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.375 |
|
|
\[
{}y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.701 |
|
|
\[
{}y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.521 |
|
|
\[
{}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.842 |
|
|
\[
{}-y+x y^{\prime } = \left (1+y^{2}\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.837 |
|
|
\[
{}y-x y^{\prime } = x y^{3} y^{\prime }
\] |
[_separable] |
✓ |
2.286 |
|
|
\[
{}x y^{\prime } = x^{5}+x^{3} y^{2}+y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.062 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.816 |
|
|
\[
{}x y^{\prime } = y+x^{2}+9 y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.593 |
|
|
\[
{}y^{2}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
2.684 |
|
|
\[
{}-y+x y^{\prime } = 2 x^{2}-3
\] |
[_linear] |
✓ |
1.439 |
|
|
\[
{}x y^{\prime }+y = \sqrt {x y}\, y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
61.393 |
|
|
\[
{}y-x y^{2}+\left (x +y^{2} x^{2}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.402 |
|
|
\[
{}-y+x y^{\prime } = x^{2} y^{4} \left (x y^{\prime }+y\right )
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.437 |
|
|
\[
{}x y^{\prime }+y+x^{2} y^{5} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.237 |
|
|
\[
{}2 x y^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.509 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.502 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
6.683 |
|
|
\[
{}x y^{\prime }-3 y = x^{4}
\] |
[_linear] |
✓ |
1.799 |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
1.886 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
1.872 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
3.033 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
1.997 |
|
|
\[
{}2 y-x^{3} = x y^{\prime }
\] |
[_linear] |
✓ |
1.811 |
|
|
\[
{}y-x +x y \cot \left (x \right )+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.989 |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.731 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
[_linear] |
✓ |
1.480 |
|
|
\[
{}y-2 x y-x^{2}+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.860 |
|
|
\[
{}x y^{\prime }+y = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.572 |
|