|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.404 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.307 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.277 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.132 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \delta \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.109 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.390 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.515 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.252 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+3 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.271 |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.967 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.248 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.249 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.397 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.531 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\sqrt {2}\, y \\ y^{\prime }=\sqrt {2}\, x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.361 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.288 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.331 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.518 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+z \\ y^{\prime }=-2 x-y+3 z \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y-z \\ y^{\prime }=2 x-y-4 z \\ z^{\prime }=3 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
7.985 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y-4 t +1 \\ y^{\prime }=-x+2 y+3 t +4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.173 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-t +3 \\ y^{\prime }=x+4 y+t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.876 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y-t +3 \\ y^{\prime }=-x-5 y+t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.096 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y+1 \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.048 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=t y+1 \\ y^{\prime }=-x t +y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
0.254 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
1.086 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.560 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.534 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.501 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.313 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.671 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.811 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.520 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.048 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.267 |
|
|
\[
{}y^{\prime \prime }-y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.487 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[_Lienard] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
0.560 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.598 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.599 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.585 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.657 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.616 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.688 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.612 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.521 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.641 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.583 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.634 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.817 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.873 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.331 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.281 |
|
|
\[
{}y^{\prime \prime }-y x = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x -4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.699 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.825 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.135 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.110 |
|
|
\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.505 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.860 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.600 |
|
|
\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.523 |
|
|
\[
{}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.753 |
|
|
\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.448 |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.142 |
|
|
\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.416 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.405 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.179 |
|