|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.224 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.300 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.227 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.622 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.679 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.546 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.513 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.557 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.799 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.195 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.333 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.431 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.183 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.585 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = -8
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.787 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.437 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.557 |
|
|
\[
{}y^{\prime \prime }+2 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.421 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.366 |
|
|
\[
{}y^{\prime \prime }+9 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.381 |
|
|
\[
{}y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.400 |
|
|
\[
{}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.045 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.113 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.135 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.200 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.326 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.327 |
|
|
\[
{}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.803 |
|
|
\[
{}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.931 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.574 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.555 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.593 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.589 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.677 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
37.554 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.414 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.021 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.760 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.644 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.778 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
42.329 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.874 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.404 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.369 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.236 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.954 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.139 |
|
|
\[
{}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.856 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.934 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.850 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.013 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.834 |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.077 |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.518 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.834 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.795 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.863 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.159 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.026 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.310 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.232 |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.310 |
|
|
\[
{}y^{\prime } = 3-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.523 |
|
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.433 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime } x = \arcsin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
19.221 |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_separable] |
✓ |
3.421 |
|
|
\[
{}y^{\prime \prime } = \frac {x +1}{x -1}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.066 |
|
|
\[
{}x^{2} y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.652 |
|
|
\[
{}y^{2} y^{\prime \prime } = 8 x^{2}
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.119 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
25.031 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.746 |
|
|
\[
{}y^{\prime } = 4 x^{3}
\] |
[_quadrature] |
✓ |
0.457 |
|
|
\[
{}y^{\prime } = 20 \,{\mathrm e}^{-4 x}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } x +\sqrt {x} = 2
\] |
[_quadrature] |
✓ |
0.443 |
|
|
\[
{}\sqrt {x +4}\, y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.572 |
|
|
\[
{}y^{\prime } = x \cos \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.540 |
|
|
\[
{}y^{\prime } = x \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}x = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.563 |
|
|
\[
{}1 = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.603 |
|
|
\[
{}1 = x^{2}-9 y^{\prime }
\] |
[_quadrature] |
✓ |
0.475 |
|
|
\[
{}y^{\prime \prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.229 |
|
|
\[
{}y^{\prime \prime }-3 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.936 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _quadrature]] |
✓ |
0.096 |
|