|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.639 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.649 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.648 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.651 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {9 x}{10}-2 y \\ y^{\prime }=x+\frac {11 y}{10} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+10 y \\ y^{\prime }=-x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.357 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.588 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.353 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.369 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.371 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.351 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=3 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.212 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.717 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{10} \\ y^{\prime }=\frac {z}{5} \\ z^{\prime }=\frac {2 x}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.925 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \\ z^{\prime }=2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.443 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=3 x-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.348 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 z \\ y^{\prime }=-y \\ z^{\prime }=-3 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 y-z \\ z^{\prime }=-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.287 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.283 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y+z \\ z^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.279 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.226 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-2 y+3 z \\ z^{\prime }=-x+3 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.842 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+3 y \\ y^{\prime }=z-y \\ z^{\prime }=5 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.668 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-10 x+10 y \\ y^{\prime }=28 x-y \\ z^{\prime }=-\frac {8 z}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.600 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z-x \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.130 |
|
|
\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.183 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.245 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.136 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.253 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.801 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.281 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-4 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.286 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.947 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.820 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.015 |
|
|
\[
{}y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
42.617 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.903 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.886 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.876 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.731 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.967 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.936 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.917 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
10.021 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.131 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.406 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.828 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
18.265 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.910 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.044 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.386 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = -8
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.527 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.802 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.349 |
|
|
\[
{}y^{\prime \prime }+2 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.202 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.490 |
|
|
\[
{}y^{\prime \prime }+9 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.138 |
|
|
\[
{}y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.888 |
|
|
\[
{}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.871 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.856 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.874 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.204 |
|
|
\[
{}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.752 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.166 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.073 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.215 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.237 |
|
|
\[
{}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.921 |
|
|
\[
{}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.110 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.225 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.233 |
|