|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (2 x -2 y+5\right ) y^{\prime }-x +y-3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.910 |
|
|
\[
{}x +y+1-\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.012 |
|
|
\[
{}y^{2} = \left (x y-x^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.398 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.743 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.869 |
|
|
\[
{}x^{2} y^{\prime }+y \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.541 |
|
|
\[
{}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.421 |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
81.902 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.069 |
|
|
\[
{}\left (2 x +4 y+3\right ) y^{\prime } = 2 y+x +1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.948 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.435 |
|
|
\[
{}x \left (x^{2}+3 y^{2}\right )+y \left (y^{2}+3 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
26.245 |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.155 |
|
|
\[
{}y^{\prime } = \frac {2 x -y+1}{x +2 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.276 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.393 |
|
|
\[
{}x -y-2-\left (2 x -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.937 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.995 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
4.470 |
|
|
\[
{}x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 1
\] |
[_linear] |
✓ |
6.336 |
|
|
\[
{}y-x \sin \left (x^{2}\right )+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.689 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 2 \ln \left (x \right )
\] |
[_linear] |
✓ |
1.174 |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y+\sin \left (x \right )
\] |
[_linear] |
✓ |
3.543 |
|
|
\[
{}\left (1+x +x y^{2}\right ) y^{\prime }+y+y^{3} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.408 |
|
|
\[
{}y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.123 |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}}
\] |
[_linear] |
✓ |
1.522 |
|
|
\[
{}y^{\prime }-\frac {\tan \left (y\right )}{x +1} = \left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
46.418 |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
1.864 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.584 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
6.056 |
|
|
\[
{}1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.403 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.428 |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
46.005 |
|
|
\[
{}y^{\prime }+\frac {y \ln \left (y\right )}{x} = \frac {y}{x^{2}}-\ln \left (y\right )^{2}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.824 |
|
|
\[
{}y^{\prime }+x = x \,{\mathrm e}^{\left (n -1\right ) y}
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.752 |
|
|
\[
{}2 y^{\prime }-y \sec \left (x \right ) = y^{3} \tan \left (x \right )
\] |
[_Bernoulli] |
✓ |
12.716 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
6.137 |
|
|
\[
{}x +y y^{\prime } = \frac {a^{2} \left (-y+x y^{\prime }\right )}{x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.571 |
|
|
\[
{}1+4 x y+2 y^{2}+\left (1+4 x y+2 x^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.729 |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.149 |
|
|
\[
{}\left (x^{4} y^{4}+y^{2} x^{2}+x y\right ) y+\left (x^{4} y^{4}-y^{2} x^{2}+x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.923 |
|
|
\[
{}y \left (x y+2 y^{2} x^{2}\right )+x \left (x y-y^{2} x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.092 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.510 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.693 |
|
|
\[
{}\left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0
\] |
[_rational] |
✓ |
1.822 |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.089 |
|
|
\[
{}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.057 |
|
|
\[
{}\frac {x +y y^{\prime }}{-y+x y^{\prime }} = \sqrt {\frac {a^{2}-x^{2}-y^{2}}{x^{2}+y^{2}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
508.325 |
|
|
\[
{}\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b} = \frac {x +y+a}{x +y+b}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
4.338 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.962 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.146 |
|
|
\[
{}y^{\prime } = \left (4 x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
6.028 |
|
|
\[
{}-y+x y^{\prime } = x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.707 |
|
|
\[
{}x y^{\prime }+y \ln \left (y\right ) = x y \,{\mathrm e}^{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.593 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.220 |
|
|
\[
{}x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.897 |
|
|
\[
{}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y}
\] |
[_rational, _Bernoulli] |
✓ |
2.351 |
|
|
\[
{}x +y y^{\prime } = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.201 |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.638 |
|
|
\[
{}y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.918 |
|
|
\[
{}{x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\] |
[_quadrature] |
✓ |
1.048 |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.931 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}+x^{2} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
1.572 |
|
|
\[
{}x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.483 |
|
|
\[
{}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.025 |
|
|
\[
{}y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.715 |
|
|
\[
{}\left (2 x +2 y+3\right ) y^{\prime } = x +y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.994 |
|
|
\[
{}y^{\prime } = \frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )}
\] |
[_separable] |
✓ |
35.228 |
|
|
\[
{}s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s}
\] |
[_separable] |
✓ |
2.046 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.497 |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )+\cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
74.459 |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
45.026 |
|
|
\[
{}x^{2}-a y = \left (a x -y^{2}\right ) y^{\prime }
\] |
[_exact, _rational] |
✓ |
1.110 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.704 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
72.090 |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
4.029 |
|
|
\[
{}y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✓ |
2.126 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right ) = x^{3}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.744 |
|
|
\[
{}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.094 |
|
|
\[
{}y^{\prime \prime }-n^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.637 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.873 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.842 |
|
|
\[
{}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.953 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.052 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.057 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }-y = 2+5 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.198 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.967 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.237 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
21.846 |
|
|
\[
{}y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
44.007 |
|