|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.231 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.731 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.122 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.173 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.085 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.848 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.787 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.835 |
|
|
\[
{}3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.814 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.243 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.102 |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.878 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.148 |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.232 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.575 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.235 |
|
|
\[
{}y^{\prime \prime }+2 x y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.614 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.442 |
|
|
\[
{}2 y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.611 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.742 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.685 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.711 |
|
|
\[
{}\left (x^{2}+1\right ) x^{2} y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.986 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.950 |
|
|
\[
{}x y^{\prime \prime }-4 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.897 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.052 |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.873 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.976 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.829 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.007 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.007 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.873 |
|
|
\[
{}9 \left (-2+x \right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (-2+x \right ) y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.388 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}y^{\prime \prime }-y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.296 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.197 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \delta \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.117 |
|
|
\[
{}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.365 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi }
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+3 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.267 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.222 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.311 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.427 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
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 |
✓ |
0.308 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.270 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.292 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\sqrt {2}\, y \\ y^{\prime }=\sqrt {2}\, x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.380 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.313 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.528 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.524 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+z \\ y^{\prime }=-2 x-y+3 z \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y-z \\ y^{\prime }=2 x-y-4 z \\ z^{\prime }=3 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
8.153 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y-4 t +1 \\ y^{\prime }=-x+2 y+3 t +4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.229 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-t +3 \\ y^{\prime }=x+4 y+t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.881 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y-t +3 \\ y^{\prime }=-x-5 y+t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.184 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y+1 \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=t y+1 \\ y^{\prime }=-x t +y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
1.832 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.609 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.362 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.573 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.013 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.821 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.921 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.176 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.583 |
|