|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.820 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.046 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.779 |
|
|
\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.976 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.944 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.010 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.906 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.113 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.079 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.797 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.920 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.245 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.783 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.796 |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.936 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.885 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.096 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.155 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
0.793 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.743 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.790 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.872 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.968 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.879 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.020 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.756 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.814 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.792 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.826 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.575 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.569 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.955 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.909 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.059 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.780 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.557 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.619 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.094 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.104 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.620 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.673 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.575 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.958 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.582 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.618 |
|
|
\[
{}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.107 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.676 |
|
|
\[
{}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.953 |
|
|
\[
{}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.960 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 y x = 10 x^{3}-2 x +5
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.689 |
|
|
\[
{}y^{\prime }-y = 1
\] |
[_quadrature] |
✓ |
0.238 |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.222 |
|
|
\[
{}y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.262 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (5 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.321 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.509 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.268 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.407 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.350 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime }-y = 1+t \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.262 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.322 |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 1+t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.441 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.242 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.168 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.446 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.502 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.530 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime }+y = t \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.389 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.555 |
|
|
\[
{}t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.151 |
|
|
\[
{}2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.071 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.440 |
|