|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.864 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.990 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.829 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.108 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.088 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.322 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.844 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.871 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.857 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.166 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.635 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.728 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
1.089 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.561 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.679 |
|
|
\[
{}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.643 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.684 |
|
|
\[
{}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.300 |
|
|
\[
{}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.012 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.716 |
|
|
\[
{}y^{\prime }-y = 1
\] |
[_quadrature] |
✓ |
0.383 |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.415 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (5 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.538 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.249 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.285 |
|
|
\[
{}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.462 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.459 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.318 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.396 |
|
|
\[
{}y^{\prime }-y = 1+t \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.455 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.237 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.237 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.267 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.287 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.295 |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.449 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 1+t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.411 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.267 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.197 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.567 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.657 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.681 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.922 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.705 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.583 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.751 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.354 |
|
|
\[
{}y^{\prime }+y = t \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.522 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.384 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.599 |
|
|
\[
{}t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.248 |
|
|
\[
{}2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.214 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.364 |
|
|
\[
{}y^{\prime }-3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.475 |
|
|
\[
{}y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.509 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.506 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.643 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.518 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.429 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.071 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.998 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=4 x+8 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.790 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-7 y \\ y^{\prime }=5 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.792 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y-9 z \\ y^{\prime }=6 x-y \\ z^{\prime }=10 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
9.994 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+2 z \\ z^{\prime }=z-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
8.373 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+z+t -1 \\ y^{\prime }=2 x+y-z-3 t^{2} \\ z^{\prime }=x+y+z+t^{2}-t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.438 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }=y+6 z-{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
178.804 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }=-x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.191 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
37.583 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
202.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
4.817 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+5 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+\frac {y}{4} \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=x+y \\ z^{\prime }=-2 x-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.629 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.466 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+2 y \\ y^{\prime }=\frac {3 x}{4}-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 x-5 y \\ y^{\prime }=8 x-12 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.432 |
|