|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.669 |
|
|
\[
{}x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
0.620 |
|
|
\[
{}2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
4.206 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.541 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.509 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.850 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.405 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.416 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.673 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.516 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.614 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.486 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.335 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.860 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.367 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.120 |
|
|
\[
{}36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.904 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+24 y^{\prime } x +\left (144 x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.872 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.662 |
|
|
\[
{}16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
33.106 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.517 |
|
|
\[
{}y^{\prime \prime }+x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.073 |
|
|
\[
{}x y^{\prime \prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.120 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.546 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
3.149 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.450 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.296 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.264 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+15 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.203 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.335 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.305 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.312 |
|
|
\[
{}x^{\prime \prime }+9 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.228 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.235 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.626 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+25 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.326 |
|
|
\[
{}x^{\prime \prime }-6 x^{\prime }+8 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.205 |
|
|
\[
{}x^{\prime \prime }-4 x = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.204 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.286 |
|
|
\[
{}x^{\prime \prime \prime \prime }-x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.356 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.611 |
|
|
\[
{}x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.463 |
|
|
\[
{}x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.429 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = {\mathrm e}^{2 t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.425 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+18 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.458 |
|
|
\[
{}x^{\prime \prime }+9 x = 6 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.286 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25} = 6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.318 |
|
|
\[
{}t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.218 |
|
|
\[
{}t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.211 |
|
|
\[
{}t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.220 |
|
|
\[
{}t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.226 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+t x = 0
\] |
[_Lienard] |
✓ |
0.219 |
|
|
\[
{}t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.261 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.512 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.829 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.675 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.223 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.422 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.283 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = t +\delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.160 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.235 |
|
|
\[
{}x^{\prime \prime }+9 x = \delta \left (t -3 \pi \right )+\cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.789 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = \delta \left (t -\pi \right )+\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.327 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.233 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.650 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.767 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.318 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.360 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 y \\ y^{\prime }=-10 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{2} \\ y^{\prime }=-8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.430 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=6 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=10 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=13 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.613 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-9 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} 10 x_{1}^{\prime }=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }=x_{1}-x_{2} \\ 10 x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.851 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.308 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+9 y \\ y^{\prime }=-2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.630 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y+2 t \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.960 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+2 y-{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+2 \sin \left (2 t \right ) \\ y^{\prime }=x-2 y-\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.855 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=4 x+5 y \\ 2 x^{\prime }-y^{\prime }=3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.394 |
|
|
\[
{}\left [\begin {array}{c} -x^{\prime }+2 y^{\prime }=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }=x-15 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.839 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-4 x+4 y-2 z \\ z^{\prime }=-4 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
72.037 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z+{\mathrm e}^{-t} \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|