|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = \left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
21.514 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2} {\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.197 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = \sin \left (t \right )+t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.530 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.704 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t}+{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.765 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 1+t^{2}+{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.334 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.309 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.046 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t^{{3}/{2}} {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.760 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }-t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.203 |
|
|
\[
{}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.235 |
|
|
\[
{}t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime }+t^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.371 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.451 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.483 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.604 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = {\mathrm e}^{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.367 |
|
|
\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.437 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.416 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.973 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.058 |
|
|
\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.749 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.135 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.864 |
|
|
\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.111 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.611 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.141 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.428 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.273 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.125 |
|
|
\[
{}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.716 |
|
|
\[
{}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.662 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.280 |
|
|
\[
{}t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.781 |
|
|
\[
{}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\] |
[_Laguerre] |
✓ |
0.994 |
|
|
\[
{}2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.803 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.958 |
|
|
\[
{}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.758 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.960 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.749 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.714 |
|
|
\[
{}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.930 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.767 |
|
|
\[
{}t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.852 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.471 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.144 |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.459 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.089 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\] |
[_Lienard] |
✓ |
0.562 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.727 |
|
|
\[
{}t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
1.118 |
|
|
\[
{}t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
1.117 |
|
|
\[
{}2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.813 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.711 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.139 |
|
|
\[
{}t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.566 |
|
|
\[
{}t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
24.172 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.316 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.490 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+7 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.431 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{4 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.730 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.425 |
|
|
\[
{}y^{\prime \prime }+y = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.427 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.369 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+7 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.577 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.488 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.506 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.386 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.472 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.428 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.430 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.522 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.353 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 2 \delta \left (t -1\right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.735 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}+3 \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.323 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.303 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+t \\ y^{\prime }=-4 x+3 y-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.933 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.661 |
|