|
# |
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‘]] |
✓ |
1.266 |
|
|
\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.303 |
|
|
\[
{}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.673 |
|
|
\[
{}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.863 |
|
|
\[
{}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.780 |
|
|
\[
{}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1152.597 |
|
|
\[
{}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.835 |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.747 |
|
|
\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.374 |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
27.605 |
|
|
\[
{}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.696 |
|
|
\[
{}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.763 |
|
|
\[
{}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
45.492 |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.933 |
|
|
\[
{}3 x +y+\left (3 y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.740 |
|
|
\[
{}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.909 |
|
|
\[
{}x \left (6 x y+5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.347 |
|
|
\[
{}3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.981 |
|
|
\[
{}2 x y-\left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.728 |
|
|
\[
{}y \cos \left (x \right )-2 \sin \left (y\right ) = \left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime }
\] |
[_exact] |
✓ |
9.870 |
|
|
\[
{}\frac {2 x y-1}{y}+\frac {\left (3 y+x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.893 |
|
|
\[
{}y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.527 |
|
|
\[
{}3 y \sin \left (x \right )-\cos \left (y\right )+\left (x \sin \left (y\right )-3 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.967 |
|
|
\[
{}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.429 |
|
|
\[
{}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.492 |
|
|
\[
{}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.556 |
|
|
\[
{}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.510 |
|
|
\[
{}y^{2} \csc \left (x \right )^{2}+6 x y-2 = \left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime }
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
48.605 |
|
|
\[
{}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
3.005 |
|
|
\[
{}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.481 |
|
|
\[
{}2 y \sin \left (x y\right )+\left (2 x \sin \left (x y\right )+y^{3}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
42.336 |
|
|
\[
{}\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_exact] |
✓ |
5.490 |
|
|
\[
{}y \,{\mathrm e}^{x y}+2 x y+\left (x \,{\mathrm e}^{x y}+x^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.050 |
|
|
\[
{}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
22.681 |
|
|
\[
{}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
29.975 |
|
|
\[
{}\frac {2 x^{2}}{y^{2}+x^{2}}+\ln \left (y^{2}+x^{2}\right )+\frac {2 x y y^{\prime }}{y^{2}+x^{2}} = 0
\] |
[_exact] |
✓ |
1.839 |
|
|
\[
{}x y^{\prime }+\ln \left (x \right )-y = 0
\] |
[_linear] |
✓ |
0.954 |
|
|
\[
{}x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.189 |
|
|
\[
{}\left (x -2 x y\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
1.541 |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.733 |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.610 |
|
|
\[
{}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.023 |
|
|
\[
{}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.811 |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.574 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.218 |
|
|
\[
{}2 x y+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.430 |
|
|
\[
{}y = x \left (x^{2} y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.895 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+y \,{\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
2.069 |
|
|
\[
{}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y
\] |
[_rational] |
✓ |
1.134 |
|
|
\[
{}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.800 |
|
|
\[
{}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
1.763 |
|
|
\[
{}y \left (1-x^{4} y^{2}\right )+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.839 |
|
|
\[
{}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.774 |
|
|
\[
{}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.878 |
|
|
\[
{}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.254 |
|
|
\[
{}y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
36.855 |
|
|
\[
{}y \left (y^{2}+x \right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
135.538 |
|
|
\[
{}x y^{\prime }+2 y = x^{2}
\] |
[_linear] |
✓ |
1.339 |
|
|
\[
{}y^{\prime }-x y = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.520 |
|
|
\[
{}y^{\prime }+2 x y = 2 x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.265 |
|
|
\[
{}y^{\prime } = y+3 x^{2} {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.450 |
|
|
\[
{}x^{\prime }+x = {\mathrm e}^{-y}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.933 |
|
|
\[
{}y x^{\prime }+\left (1+y \right ) x = {\mathrm e}^{y}
\] |
[_linear] |
✓ |
1.208 |
|
|
\[
{}y+\left (2 x -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.032 |
|
|
\[
{}x y^{\prime }-2 x^{4}-2 y = 0
\] |
[_linear] |
✓ |
1.337 |
|
|
\[
{}1 = \left ({\mathrm e}^{y}+x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.114 |
|
|
\[
{}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1
\] |
[_linear] |
✓ |
1.973 |
|
|
\[
{}x y^{\prime } = 5 y+x +1
\] |
[_linear] |
✓ |
1.427 |
|
|
\[
{}x^{2} y^{\prime }+y-2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
1.499 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {{\mathrm e}^{x}}{x +1}
\] |
[_linear] |
✓ |
1.569 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.841 |
|
|
\[
{}2 y = \left (y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.289 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right )
\] |
[_linear] |
✓ |
1.784 |
|
|
\[
{}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right )
\] |
[_linear] |
✓ |
4.957 |
|
|
\[
{}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right )
\] |
[_linear] |
✓ |
1.812 |
|
|
\[
{}y^{2}+1+\left (2 x y-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.133 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right )-\sec \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.497 |
|
|
\[
{}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.714 |
|
|
\[
{}2 y-x y-3+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.389 |
|
|
\[
{}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.950 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0
\] |
[_linear] |
✓ |
1.500 |
|
|
\[
{}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.276 |
|
|
\[
{}y^{3} y^{\prime }+x y^{4} = x \,{\mathrm e}^{-x^{2}}
\] |
[_Bernoulli] |
✓ |
3.277 |
|
|
\[
{}\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.058 |
|
|
\[
{}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.499 |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.385 |
|
|
\[
{}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}}
\] |
[_Bernoulli] |
✓ |
1.543 |
|
|
\[
{}x^{\prime } t +x \left (1-x^{2} t^{4}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.324 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.799 |
|
|
\[
{}\csc \left (y\right ) \cot \left (y\right ) y^{\prime } = \csc \left (y\right )+{\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.434 |
|
|
\[
{}y^{\prime }-x y = \frac {x}{y}
\] |
[_separable] |
✓ |
1.549 |
|
|
\[
{}y+x y^{\prime } = y^{2} x^{2} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.083 |
|
|
\[
{}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0
\] |
[_separable] |
✓ |
1.562 |
|
|
\[
{}x y^{\prime }+2 y = 3 x^{3} y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
7.084 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
2.200 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
39.707 |
|
|
\[
{}\left (x \tan \left (y\right )^{2}+x \right ) y^{\prime } = 2 x^{2}+\tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.595 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.138 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{-t}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.602 |
|
|
\[
{}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.040 |
|