|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.634 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.971 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.945 |
|
|
\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.088 |
|
|
\[
{}2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.091 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.955 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.842 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.975 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.996 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.988 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.894 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.615 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.067 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.636 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.723 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.042 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.255 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.273 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.134 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.282 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.219 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 y x = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.911 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.199 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y = x^{2}-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y = x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.977 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.208 |
|
|
\[
{}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.418 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = x^{4}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.145 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.996 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.731 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 6 \left (-x^{2}+1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.220 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.886 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = x \left (x^{2}+x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.770 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = x^{2} \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.936 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.235 |
|
|
\[
{}y^{\prime } = 2 \,{\mathrm e}^{3 x}
\] |
[_quadrature] |
✓ |
0.147 |
|
|
\[
{}y^{\prime } = \frac {2}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.685 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.149 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.646 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.148 |
|
|
\[
{}y^{\prime } = y x
\] |
[_separable] |
✓ |
1.839 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
2.428 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
2.470 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.553 |
|
|
\[
{}y^{\prime } x = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.821 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
1.687 |
|
|
\[
{}{y^{\prime }}^{2}-3 y^{\prime }+2 = 0
\] |
[_quadrature] |
✓ |
0.957 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.181 |
|
|
\[
{}y^{\prime } \sin \left (x \right ) = 1
\] |
[_quadrature] |
✓ |
0.826 |
|
|
\[
{}y^{\prime } = t^{2}+3
\] |
[_quadrature] |
✓ |
0.129 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.720 |
|
|
\[
{}y^{\prime } = \sin \left (3 t \right )
\] |
[_quadrature] |
✓ |
0.182 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.180 |
|
|
\[
{}y^{\prime } = \frac {t}{t^{2}+4}
\] |
[_quadrature] |
✓ |
0.687 |
|
|
\[
{}y^{\prime } = \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.131 |
|
|
\[
{}y^{\prime } = \frac {t}{\sqrt {t}+1}
\] |
[_quadrature] |
✓ |
0.178 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
0.976 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
0.917 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y}
\] |
[_separable] |
✓ |
2.285 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.247 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.892 |
|
|
\[
{}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}y^{\prime } = \frac {y}{t}
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
5.954 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.030 |
|
|
\[
{}y^{\prime } = y-1
\] |
[_quadrature] |
✓ |
0.170 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.806 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
1.078 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
0.217 |
|
|
\[
{}y^{\prime } = \left (t^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.920 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
0.852 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.190 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.665 |
|
|
\[
{}y^{\prime } = t -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.098 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.169 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
2.208 |
|
|
\[
{}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1
\] |
[_linear] |
✓ |
2.394 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3}
\] |
[_linear] |
✓ |
2.378 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.001 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.135 |
|
|
\[
{}t y^{\prime } = y+t^{3}
\] |
[_linear] |
✓ |
2.128 |
|
|
\[
{}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
2.409 |
|
|
\[
{}y^{\prime } = \frac {2 y}{1+t}
\] |
[_separable] |
✓ |
2.616 |
|
|
\[
{}t y^{\prime } = -y+t^{3}
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right )
\] |
[_separable] |
✓ |
3.601 |
|
|
\[
{}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y
\] |
[_linear] |
✓ |
1.639 |
|
|
\[
{}y^{\prime } = \frac {2 y}{-t^{2}+1}+3
\] |
[_linear] |
✓ |
2.296 |
|
|
\[
{}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
3.000 |
|
|
\[
{}y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
3.727 |
|
|
\[
{}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
4.263 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = 4 y^{2}
\] |
[_separable] |
✓ |
3.018 |
|
|
\[
{}y \left (2 x^{2} y^{2}+1\right ) y^{\prime }+x \left (y^{4}+1\right ) = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.854 |
|
|
\[
{}2 y^{\prime } x +3 x +y = 0
\] |
[_linear] |
✓ |
7.181 |
|
|
\[
{}\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.612 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+4 y x = \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
8.431 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
4.393 |
|
|
\[
{}\left (x +y^{3}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
11.244 |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{y x}
\] |
[_rational, _Bernoulli] |
✓ |
2.349 |
|
|
\[
{}\left (-x +y\right ) y^{\prime }+2 x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.168 |
|