|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.183 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.129 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.124 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.554 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.640 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.649 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.568 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.651 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-4 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.858 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.235 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.155 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.422 |
|
|
\[
{}y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
19.759 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.198 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
14.160 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.041 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.174 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.006 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.398 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.603 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.276 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.174 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.188 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.062 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.146 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.246 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.993 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.451 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = -8
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.657 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.444 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.366 |
|
|
\[
{}y^{\prime \prime }+2 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.374 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.309 |
|
|
\[
{}y^{\prime \prime }+9 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.128 |
|
|
\[
{}y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.437 |
|
|
\[
{}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.691 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.066 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.088 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.206 |
|
|
\[
{}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.682 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.042 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.137 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.112 |
|
|
\[
{}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.357 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.400 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.398 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.521 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
33.909 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
53.283 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.945 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.686 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.302 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.721 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.396 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
43.904 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.462 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.012 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.498 |
|
|
\[
{}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.274 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.984 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.951 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.635 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.408 |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.629 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.603 |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.931 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.586 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.943 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.618 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.289 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.241 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.489 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.386 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.236 |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}y^{\prime } = 3-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.580 |
|