|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x -y+1+\left (x -y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.773 |
|
|
\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.838 |
|
|
\[
{}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.142 |
|
|
\[
{}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.116 |
|
|
\[
{}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.391 |
|
|
\[
{}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1460.432 |
|
|
\[
{}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.347 |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.320 |
|
|
\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.477 |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
49.512 |
|
|
\[
{}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.233 |
|
|
\[
{}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.207 |
|
|
\[
{}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
85.084 |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.010 |
|
|
\[
{}3 x +y+\left (x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.881 |
|
|
\[
{}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.700 |
|
|
\[
{}x \left (6 x y+5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.337 |
|
|
\[
{}3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.050 |
|
|
\[
{}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.181 |
|
|
\[
{}y \cos \left (x \right )-2 \sin \left (y\right ) = \left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime }
\] |
[_exact] |
✓ |
10.455 |
|
|
\[
{}\frac {2 x y-1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.934 |
|
|
\[
{}y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.737 |
|
|
\[
{}3 y \sin \left (x \right )-\cos \left (y\right )+\left (x \sin \left (y\right )-3 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
39.391 |
|
|
\[
{}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.461 |
|
|
\[
{}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.914 |
|
|
\[
{}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.698 |
|
|
\[
{}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.546 |
|
|
\[
{}y^{2} \csc \left (x \right )^{2}+6 x y-2 = \left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime }
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
52.042 |
|
|
\[
{}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
3.108 |
|
|
\[
{}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.158 |
|
|
\[
{}2 y \sin \left (x y\right )+\left (2 x \sin \left (x y\right )+y^{3}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
42.911 |
|
|
\[
{}\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_exact] |
✓ |
5.923 |
|
|
\[
{}y \,{\mathrm e}^{x y}+2 x y+\left (x \,{\mathrm e}^{x y}+x^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.140 |
|
|
\[
{}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
20.906 |
|
|
\[
{}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
26.920 |
|
|
\[
{}\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}} = 0
\] |
[_exact] |
✓ |
1.831 |
|
|
\[
{}y^{\prime } x +\ln \left (x \right )-y = 0
\] |
[_linear] |
✓ |
1.146 |
|
|
\[
{}x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.362 |
|
|
\[
{}\left (x -2 x y\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
1.885 |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.950 |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.827 |
|
|
\[
{}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.277 |
|
|
\[
{}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.166 |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.750 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.139 |
|
|
\[
{}2 x y+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.657 |
|
|
\[
{}y = x \left (x^{2} y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.647 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+y \,{\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
2.288 |
|
|
\[
{}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y
\] |
[_rational] |
✓ |
1.206 |
|
|
\[
{}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.974 |
|
|
\[
{}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
1.944 |
|
|
\[
{}y \left (1-x^{4} y^{2}\right )+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.924 |
|
|
\[
{}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.165 |
|
|
\[
{}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.101 |
|
|
\[
{}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.419 |
|
|
\[
{}y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
36.641 |
|
|
\[
{}y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
193.409 |
|
|
\[
{}y^{\prime } x +2 y = x^{2}
\] |
[_linear] |
✓ |
1.668 |
|
|
\[
{}y^{\prime }-x y = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.710 |
|
|
\[
{}y^{\prime }+2 x y = 2 x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.463 |
|
|
\[
{}y^{\prime } = y+3 x^{2} {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.694 |
|
|
\[
{}x^{\prime }+x = {\mathrm e}^{-y}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.171 |
|
|
\[
{}y x^{\prime }+\left (1+y \right ) x = {\mathrm e}^{y}
\] |
[_linear] |
✓ |
1.366 |
|
|
\[
{}y+\left (2 x -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.743 |
|
|
\[
{}y^{\prime } x -2 x^{4}-2 y = 0
\] |
[_linear] |
✓ |
1.603 |
|
|
\[
{}1 = \left ({\mathrm e}^{y}+x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.275 |
|
|
\[
{}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1
\] |
[_linear] |
✓ |
2.173 |
|
|
\[
{}y^{\prime } x = 5 y+x +1
\] |
[_linear] |
✓ |
1.740 |
|
|
\[
{}x^{2} y^{\prime }+y-2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
1.697 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {{\mathrm e}^{x}}{x +1}
\] |
[_linear] |
✓ |
1.728 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.088 |
|
|
\[
{}2 y = \left (y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.463 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right )
\] |
[_linear] |
✓ |
1.952 |
|
|
\[
{}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right )
\] |
[_linear] |
✓ |
5.210 |
|
|
\[
{}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right )
\] |
[_linear] |
✓ |
1.992 |
|
|
\[
{}y^{2}+1+\left (2 x y-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.274 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right )-\sec \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.668 |
|
|
\[
{}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.802 |
|
|
\[
{}2 y-x y-3+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.566 |
|
|
\[
{}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.169 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0
\] |
[_linear] |
✓ |
1.680 |
|
|
\[
{}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.391 |
|
|
\[
{}y^{3} y^{\prime }+x y^{4} = x \,{\mathrm e}^{-x^{2}}
\] |
[_Bernoulli] |
✓ |
3.491 |
|
|
\[
{}\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.169 |
|
|
\[
{}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.587 |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.851 |
|
|
\[
{}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}}
\] |
[_Bernoulli] |
✓ |
1.495 |
|
|
\[
{}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.601 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.375 |
|
|
\[
{}\csc \left (y\right ) \cot \left (y\right ) y^{\prime } = \csc \left (y\right )+{\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.532 |
|
|
\[
{}y^{\prime }-x y = \frac {x}{y}
\] |
[_separable] |
✓ |
1.809 |
|
|
\[
{}y+y^{\prime } x = y^{2} x^{2} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.296 |
|
|
\[
{}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0
\] |
[_separable] |
✓ |
1.782 |
|
|
\[
{}y^{\prime } x +2 y = 3 x^{3} y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
7.212 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
2.355 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
40.341 |
|
|
\[
{}\left (x \tan \left (y\right )^{2}+x \right ) y^{\prime } = 2 x^{2}+\tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.755 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.180 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{-t}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.685 |
|
|
\[
{}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.088 |
|