|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0
\] |
[_separable] |
✓ |
1.519 |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = \cot \left (y\right )
\] |
[_separable] |
✓ |
2.354 |
|
|
\[
{}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}}
\] |
[_separable] |
✓ |
2.554 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
2.887 |
|
|
\[
{}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
5.988 |
|
|
\[
{}y^{2} y^{\prime } = 2+3 y^{6}
\] |
[_quadrature] |
✓ |
11.630 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.037 |
|
|
\[
{}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )}
\] |
[_separable] |
✓ |
2.146 |
|
|
\[
{}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.277 |
|
|
\[
{}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.811 |
|
|
\[
{}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.691 |
|
|
\[
{}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
22.667 |
|
|
\[
{}x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.102 |
|
|
\[
{}y^{\prime }+\frac {x}{y}+2 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.182 |
|
|
\[
{}y^{\prime } x -y = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.079 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.139 |
|
|
\[
{}y^{\prime } x = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.895 |
|
|
\[
{}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.063 |
|
|
\[
{}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.406 |
|
|
\[
{}x^{2}-x y+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.780 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.765 |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{x -y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.423 |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.357 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.531 |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 x y+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
51.047 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.638 |
|
|
\[
{}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.581 |
|
|
\[
{}x y^{2}+x -2 y+3+\left (x^{2} y-2 x -2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.526 |
|
|
\[
{}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.372 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.135 |
|
|
\[
{}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
35.137 |
|
|
\[
{}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 x y-y \sin \left (2 x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.158 |
|
|
\[
{}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
71.986 |
|
|
\[
{}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.921 |
|
|
\[
{}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.871 |
|
|
\[
{}4 x y+3 y^{2}-x +x \left (x +2 y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.479 |
|
|
\[
{}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.384 |
|
|
\[
{}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.470 |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.275 |
|
|
\[
{}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.408 |
|
|
\[
{}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.661 |
|
|
\[
{}2+y^{2}+2 x +2 y^{\prime } y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.557 |
|
|
\[
{}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.405 |
|
|
\[
{}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.255 |
|
|
\[
{}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.165 |
|
|
\[
{}x^{2}+y+y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.635 |
|
|
\[
{}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
80.112 |
|
|
\[
{}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.598 |
|
|
\[
{}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.029 |
|
|
\[
{}y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
2.342 |
|
|
\[
{}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.856 |
|
|
\[
{}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
51.277 |
|
|
\[
{}2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.020 |
|
|
\[
{}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.756 |
|
|
\[
{}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.270 |
|
|
\[
{}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.158 |
|
|
\[
{}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.394 |
|
|
\[
{}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
12.016 |
|
|
\[
{}1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.360 |
|
|
\[
{}\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.552 |
|
|
\[
{}1-\left (y-2 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.569 |
|
|
\[
{}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.397 |
|
|
\[
{}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.056 |
|
|
\[
{}1+\left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.225 |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.283 |
|
|
\[
{}y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.530 |
|
|
\[
{}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3}
\] |
[_linear] |
✓ |
0.241 |
|
|
\[
{}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}y^{\prime } = 1+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
0.345 |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )
\] |
[_linear] |
✓ |
0.355 |
|
|
\[
{}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
0.348 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y = x \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
0.243 |
|
|
\[
{}1+y+\left (x -y \left (1+y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.981 |
|
|
\[
{}y^{\prime }+y^{2} = x^{2}+1
\] |
[_Riccati] |
✓ |
0.430 |
|
|
\[
{}3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y = 0
\] |
[_Bernoulli] |
✓ |
0.721 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.064 |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
0.494 |
|
|
\[
{}\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
0.322 |
|
|
\[
{}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
0.483 |
|
|
\[
{}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
0.523 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
0.368 |
|
|
\[
{}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.427 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.584 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.469 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime }
\] |
[_quadrature] |
✓ |
0.271 |
|
|
\[
{}x y^{\prime } \left (y^{\prime }+2\right ) = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.187 |
|
|
\[
{}x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
1.006 |
|
|
\[
{}2 {y^{\prime }}^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.554 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
109.105 |
|
|
\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.526 |
|
|
\[
{}2 y^{\prime } x -y = y^{\prime } \ln \left (y^{\prime } y\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.313 |
|
|
\[
{}y = y^{\prime } x -x^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
13.467 |
|
|
\[
{}y \left (y-2 y^{\prime } x \right )^{3} = {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
119.430 |
|
|
\[
{}y^{\prime } x +y = 4 \sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
2.226 |
|
|
\[
{}2 y^{\prime } x -y = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
7.971 |
|
|
\[
{}x y^{2} \left (y^{\prime } x +y\right ) = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.754 |
|
|
\[
{}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.421 |
|
|
\[
{}y^{\prime } = \frac {y+2}{x +1}
\] |
[_separable] |
✓ |
1.886 |
|
|
\[
{}y^{\prime } x = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.007 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
6.049 |
|