|
# |
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]] |
✓ |
0.915 |
|
|
\[
{}x y^{\prime \prime }-\left (4+x \right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
0.983 |
|
|
\[
{}2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.375 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.948 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.946 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.711 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.819 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.049 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.472 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.039 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.869 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.647 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.960 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.526 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.903 |
|
|
\[
{}36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.329 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.731 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.500 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.883 |
|
|
\[
{}16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.773 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.566 |
|
|
\[
{}y^{\prime \prime }+x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.011 |
|
|
\[
{}x y^{\prime \prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.940 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.656 |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.091 |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.968 |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.547 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.292 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.333 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.275 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+15 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.310 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.365 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.355 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.382 |
|
|
\[
{}x^{\prime \prime }+9 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.323 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+25 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.348 |
|
|
\[
{}x^{\prime \prime }-6 x^{\prime }+8 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.283 |
|
|
\[
{}x^{\prime \prime }-4 x = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.321 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.294 |
|
|
\[
{}x^{\prime \prime \prime \prime }-x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.369 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.673 |
|
|
\[
{}x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.504 |
|
|
\[
{}x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.486 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = {\mathrm e}^{2 t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.515 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.464 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+18 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}x^{\prime \prime }+9 x = 6 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.317 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25} = 6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.355 |
|
|
\[
{}t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0
\] |
[[_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]] |
✓ |
0.217 |
|
|
\[
{}t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.229 |
|
|
\[
{}t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.236 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+x t = 0
\] |
[_Lienard] |
✓ |
0.246 |
|
|
\[
{}t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.271 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.070 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.683 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.988 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.253 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.764 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = t +\delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.245 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.499 |
|
|
\[
{}x^{\prime \prime }+9 x = \delta \left (t -3 \pi \right )+\cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.622 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = \delta \left (t -\pi \right )+\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.014 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.885 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.070 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.682 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.689 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.661 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.311 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 y \\ y^{\prime }=-10 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.423 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{2} \\ y^{\prime }=-8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=6 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=10 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=13 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-9 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.318 |
|
|
\[
{}\left [\begin {array}{c} 10 x_{1}^{\prime }=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }=x_{1}-x_{2} \\ 10 x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.937 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.306 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
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 |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+9 y \\ y^{\prime }=-2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y+2 t \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+2 y-{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+2 \sin \left (2 t \right ) \\ y^{\prime }=x-2 y-\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.706 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=4 x+5 y \\ 2 x^{\prime }-y^{\prime }=3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} -x^{\prime }+2 y^{\prime }=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }=x-15 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.896 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-4 x+4 y-2 z \\ z^{\prime }=-4 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
54.758 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z+{\mathrm e}^{-t} \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.598 |
|