|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
0.493 |
|
|
\[
{}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.645 |
|
|
\[
{}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.561 |
|
|
\[
{}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.401 |
|
|
\[
{}z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (1+z \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.720 |
|
|
\[
{}z y^{\prime \prime }-2 y^{\prime }+y z = 0
\] |
[_Lienard] |
✓ |
0.580 |
|
|
\[
{}y^{\prime \prime }-2 z y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.333 |
|
|
\[
{}z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0
\] |
[_Jacobi] |
✓ |
0.807 |
|
|
\[
{}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.668 |
|
|
\[
{}\left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.447 |
|
|
\[
{}\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.435 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{z^{3}} = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.088 |
|
|
\[
{}z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
0.763 |
|
|
\[
{}\left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.515 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.630 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.933 |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
2.505 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (x \right ) x}
\] |
[_separable] |
✓ |
1.517 |
|
|
\[
{}y-\left (-2+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.799 |
|
|
\[
{}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}y-x y^{\prime } = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.914 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1
\] |
[_separable] |
✓ |
2.799 |
|
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (-1+x \right )}
\] |
[_separable] |
✓ |
2.757 |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32
\] |
[_linear] |
✓ |
1.725 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
2.059 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.896 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
2.099 |
|
|
\[
{}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )}
\] |
[_separable] |
✓ |
3.961 |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.812 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.325 |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
1.739 |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_linear] |
✓ |
1.585 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = 4 x
\] |
[_linear] |
✓ |
1.974 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.053 |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
3.814 |
|
|
\[
{}y^{\prime }+\frac {y}{\ln \left (x \right ) x} = 9 x^{2}
\] |
[_linear] |
✓ |
1.256 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
2.390 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.387 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
2.338 |
|
|
\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
2.069 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
1.363 |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.933 |
|
|
\[
{}y^{\prime }+\frac {m}{x} = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.280 |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.293 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.575 |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.161 |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
88.767 |
|
|
\[
{}x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.680 |
|
|
\[
{}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.010 |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.914 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
64.206 |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
5.408 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.231 |
|
|
\[
{}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.148 |
|
|
\[
{}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
85.574 |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.914 |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.397 |
|
|
\[
{}y^{\prime \prime }-25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.996 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.230 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
1.922 |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}
\] |
[_separable] |
✓ |
2.219 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.484 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.990 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.183 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.869 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
29.071 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.553 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.994 |
|
|
\[
{}y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
42.861 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.574 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.850 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.965 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.232 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.860 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.091 |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{2+2 x y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.500 |
|
|
\[
{}y^{\prime } = \frac {\left (1-y \,{\mathrm e}^{x y}\right ) {\mathrm e}^{-x y}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.649 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
37.886 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y}
\] |
[_Bernoulli] |
✓ |
42.810 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.833 |
|
|
\[
{}y^{\prime \prime } = x^{n}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.862 |
|
|
\[
{}y^{\prime } = x^{2} \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.493 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.726 |
|
|
\[
{}y^{\prime \prime \prime } = 6 x
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.634 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.751 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.875 |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
2.489 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (x \right ) x}
\] |
[_separable] |
✓ |
1.497 |
|
|
\[
{}y-\left (-1+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.754 |
|
|
\[
{}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
1.598 |
|
|
\[
{}y-x y^{\prime } = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.829 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1
\] |
[_separable] |
✓ |
2.671 |
|