|
# |
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]] |
✓ |
0.681 |
|
|
\[
{}x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
0.748 |
|
|
\[
{}2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.328 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.714 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.658 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.424 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.510 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.652 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.707 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.372 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.735 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.660 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.564 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.712 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.722 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.287 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.741 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.733 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.681 |
|
|
\[
{}16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.296 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime \prime }+x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.750 |
|
|
\[
{}x y^{\prime \prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.799 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.388 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.238 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
2.061 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.533 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.322 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.362 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.301 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+15 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.326 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.382 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.370 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.372 |
|
|
\[
{}x^{\prime \prime }+9 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.325 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.230 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.551 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+25 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.318 |
|
|
\[
{}x^{\prime \prime }-6 x^{\prime }+8 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.293 |
|
|
\[
{}x^{\prime \prime }-4 x = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.234 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.398 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}x^{\prime \prime \prime \prime }-x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.398 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.690 |
|
|
\[
{}x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.546 |
|
|
\[
{}x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.444 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = {\mathrm e}^{2 t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.473 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.430 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+18 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.541 |
|
|
\[
{}x^{\prime \prime }+9 x = 6 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.338 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25} = 6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.375 |
|
|
\[
{}t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.212 |
|
|
\[
{}t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.208 |
|
|
\[
{}t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.265 |
|
|
\[
{}t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.205 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+t x = 0
\] |
[_Lienard] |
✓ |
0.237 |
|
|
\[
{}t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.774 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.410 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.281 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.573 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.773 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = t +\delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.272 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.694 |
|
|
\[
{}x^{\prime \prime }+9 x = \delta \left (t -3 \pi \right )+\cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.670 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = \delta \left (t -\pi \right )+\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.706 |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.776 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.416 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.406 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.671 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 y \\ y^{\prime }=-10 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{2} \\ y^{\prime }=-8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=6 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=10 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.583 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=13 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-9 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} 10 x_{1}^{\prime }=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }=x_{1}-x_{2} \\ 10 x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.856 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.594 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.563 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.547 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+9 y \\ y^{\prime }=-2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.617 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y+2 t \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+2 y-{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+2 \sin \left (2 t \right ) \\ y^{\prime }=x-2 y-\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.779 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=4 x+5 y \\ 2 x^{\prime }-y^{\prime }=3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} -x^{\prime }+2 y^{\prime }=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }=x-15 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.004 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.542 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-4 x+4 y-2 z \\ z^{\prime }=-4 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
59.170 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z+{\mathrm e}^{-t} \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.644 |
|