|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+y^{\prime }+x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.785 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.073 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x +\left (x^{4}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.240 |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.004 |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.051 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.240 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y = 0
\] |
[_Laguerre] |
✓ |
1.315 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.025 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (5+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.032 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.922 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y = 0
\] |
[_Gegenbauer] |
✓ |
0.655 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.017 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -8 y = 0
\] |
[_erf] |
✓ |
0.567 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.951 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.146 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.990 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.933 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.599 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.095 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.003 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.734 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.010 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.915 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.912 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
1.171 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.048 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.966 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
1.195 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
1.201 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.032 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.213 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.832 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.245 |
|
|
\[
{}y x -1+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
0.183 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.976 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.925 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.333 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.571 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}
\] |
[_separable] |
✓ |
3.225 |
|
|
\[
{}y^{\prime } = x \left (\cos \left (y\right )+y\right )
\] |
[_separable] |
✓ |
1.459 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}
\] |
[_separable] |
✓ |
3.554 |
|
|
\[
{}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )
\] |
[_separable] |
✓ |
17.122 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.309 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.215 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.210 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.434 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}y^{\prime } = 1+\frac {\sec \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.778 |
|
|
\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
[_linear] |
✓ |
10.546 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
1.884 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
1.435 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
1.575 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.235 |
|
|
\[
{}y^{\prime } = \frac {-y x -1}{4 x^{3} y-2 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.373 |
|
|
\[
{}\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.299 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {1+y}{y^{2}}}
\] |
[_quadrature] |
✓ |
1.933 |
|
|
\[
{}y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.674 |
|
|
\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3}
\] |
[_Bernoulli] |
✓ |
1.816 |
|
|
\[
{}y^{\prime } = \sqrt {y}+x
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
4.699 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.171 |
|
|
\[
{}y = y^{\prime } x +x^{2} {y^{\prime }}^{2}
\] |
[_separable] |
✓ |
0.816 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } x = 0
\] |
[_quadrature] |
✓ |
0.338 |
|
|
\[
{}\frac {y^{\prime }}{x +y} = 0
\] |
[_quadrature] |
✓ |
0.327 |
|
|
\[
{}\frac {y^{\prime }}{x} = 0
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.321 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.450 |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-y x +y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.189 |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.134 |
|
|
\[
{}y^{\prime } = \frac {1}{1-y}
\] |
[_quadrature] |
✓ |
0.345 |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
1.205 |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.514 |
|
|
\[
{}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
[_Clairaut] |
✓ |
3.075 |
|
|
\[
{}y^{\prime } x -2 y+b y^{2} = c \,x^{4}
\] |
[_rational, _Riccati] |
✓ |
1.442 |
|
|
\[
{}y^{\prime } x -y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.917 |
|
|
\[
{}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\] |
[_rational, _Riccati] |
✓ |
0.294 |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.648 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.770 |
|
|
\[
{}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.595 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.563 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.807 |
|
|
\[
{}y = x {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.316 |
|
|
\[
{}y y^{\prime } = 1-x {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
0.205 |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.098 |
|
|
\[
{}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.257 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.719 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.790 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.968 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.596 |
|