|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.502 |
|
|
\[
{}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.003 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.062 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.972 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.382 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.357 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.419 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.418 |
|
|
\[
{}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.053 |
|
|
\[
{}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.233 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.438 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.370 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.391 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.389 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.494 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
39.117 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.783 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
23.078 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.462 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.760 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.860 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
40.249 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.800 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.217 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.529 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.976 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.980 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.263 |
|
|
\[
{}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.875 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.876 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.720 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.290 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.190 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.225 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.989 |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.563 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.995 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.750 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.510 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.000 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.400 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.239 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime } = 3-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.346 |
|
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.198 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.073 |
|
|
\[
{}x y^{\prime } = \arcsin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
19.700 |
|
|
\[
{}y^{\prime } y = 2 x
\] |
[_separable] |
✓ |
2.944 |
|
|
\[
{}y^{\prime \prime } = \frac {x +1}{x -1}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.505 |
|
|
\[
{}x^{2} y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.691 |
|
|
\[
{}y^{2} y^{\prime \prime } = 8 x^{2}
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.089 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.977 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.792 |
|
|
\[
{}y^{\prime } = 4 x^{3}
\] |
[_quadrature] |
✓ |
0.266 |
|
|
\[
{}y^{\prime } = 20 \,{\mathrm e}^{-4 x}
\] |
[_quadrature] |
✓ |
0.319 |
|
|
\[
{}x y^{\prime }+\sqrt {x} = 2
\] |
[_quadrature] |
✓ |
0.334 |
|
|
\[
{}\sqrt {4+x}\, y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}y^{\prime } = x \cos \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}y^{\prime } = x \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.343 |
|
|
\[
{}x = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}1 = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.418 |
|
|
\[
{}1 = x^{2}-9 y^{\prime }
\] |
[_quadrature] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.675 |
|
|
\[
{}y^{\prime \prime }-3 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.328 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _quadrature]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime } = 40 x \,{\mathrm e}^{2 x}
\] |
[_quadrature] |
✓ |
0.506 |
|
|
\[
{}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.658 |
|
|
\[
{}y^{\prime } = \frac {x -1}{x +1}
\] |
[_quadrature] |
✓ |
0.538 |
|
|
\[
{}x y^{\prime }+2 = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.640 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
1.064 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.543 |
|
|
\[
{}x y^{\prime \prime }+2 = \sqrt {x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.653 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.334 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.507 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.575 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.304 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.513 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}+5}}
\] |
[_quadrature] |
✓ |
0.804 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-9 x^{2}}
\] |
[_quadrature] |
✓ |
0.445 |
|
|
\[
{}x y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.622 |
|
|
\[
{}x y^{\prime } = \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.664 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.292 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.296 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.314 |
|
|
\[
{}y^{\prime }+3 x y = 6 x
\] |
[_separable] |
✓ |
1.180 |
|