|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y+\sin \left (x \right )
\] |
[_linear] |
✓ |
2.934 |
|
|
\[
{}\left (1+x +x y^{2}\right ) y^{\prime }+y+y^{3} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.341 |
|
|
\[
{}y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
1.829 |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}}
\] |
[_linear] |
✓ |
1.411 |
|
|
\[
{}y^{\prime }-\frac {\tan \left (y\right )}{x +1} = \left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
44.417 |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
1.625 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.413 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.403 |
|
|
\[
{}1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.278 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.297 |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
43.503 |
|
|
\[
{}y^{\prime }+\frac {y \ln \left (y\right )}{x} = \frac {y}{x^{2}}-\ln \left (y\right )^{2}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.559 |
|
|
\[
{}y^{\prime }+x = x \,{\mathrm e}^{\left (n -1\right ) y}
\] |
[_separable] |
✓ |
1.546 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.220 |
|
|
\[
{}2 y^{\prime }-y \sec \left (x \right ) = y^{3} \tan \left (x \right )
\] |
[_Bernoulli] |
✓ |
11.379 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
4.795 |
|
|
\[
{}x +y y^{\prime } = \frac {a^{2} \left (-y+y^{\prime } x \right )}{x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.440 |
|
|
\[
{}1+4 x y+2 y^{2}+\left (1+4 x y+2 x^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.485 |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.020 |
|
|
\[
{}\left (x^{4} y^{4}+x^{2} y^{2}+x y\right ) y+\left (x^{4} y^{4}-x^{2} y^{2}+x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.059 |
|
|
\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.805 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.020 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.764 |
|
|
\[
{}\left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0
\] |
[_rational] |
✓ |
1.767 |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.635 |
|
|
\[
{}2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.978 |
|
|
\[
{}\frac {x +y y^{\prime }}{-y+y^{\prime } x} = \sqrt {\frac {a^{2}-x^{2}-y^{2}}{x^{2}+y^{2}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
332.481 |
|
|
\[
{}\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b} = \frac {x +y+a}{x +y+b}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
3.552 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.256 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.328 |
|
|
\[
{}y^{\prime } = \left (4 x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
6.646 |
|
|
\[
{}-y+y^{\prime } x = x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
4.024 |
|
|
\[
{}y^{\prime } x +y \ln \left (y\right ) = x y \,{\mathrm e}^{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.341 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.353 |
|
|
\[
{}x \left (x^{2}+y^{2}-a^{2}\right )+\left (x^{2}-y^{2}-b^{2}\right ) y y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.658 |
|
|
\[
{}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y}
\] |
[_rational, _Bernoulli] |
✓ |
2.007 |
|
|
\[
{}x +y y^{\prime } = m \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.701 |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.325 |
|
|
\[
{}y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.827 |
|
|
\[
{}{x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\] |
[_quadrature] |
✓ |
0.364 |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.246 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
1.441 |
|
|
\[
{}x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.351 |
|
|
\[
{}2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.257 |
|
|
\[
{}y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.886 |
|
|
\[
{}\left (2 x +2 y+3\right ) y^{\prime } = x +y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.851 |
|
|
\[
{}y^{\prime } = \frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )}
\] |
[_separable] |
✓ |
34.681 |
|
|
\[
{}s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s}
\] |
[_separable] |
✓ |
1.827 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.168 |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )+\cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
150.448 |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
43.530 |
|
|
\[
{}x^{2}-a y = \left (a x -y^{2}\right ) y^{\prime }
\] |
[_exact, _rational] |
✓ |
1.059 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.210 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
18.089 |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
3.293 |
|
|
\[
{}y-y^{\prime } x +x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✓ |
1.783 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right ) = x^{3}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.118 |
|
|
\[
{}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.554 |
|
|
\[
{}y^{\prime \prime }-n^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.051 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.070 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.202 |
|
|
\[
{}y^{\prime \prime }-y = 2+5 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.101 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.399 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.780 |
|
|
\[
{}y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.072 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.670 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.591 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.760 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y = \cos \left (4 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.664 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.408 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.103 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = x^{2}+1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
20.615 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
43.392 |
|
|
\[
{}y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.041 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+y = a \,x^{2}+b \,{\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.476 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.720 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.702 |
|