Can we solve the following ODE system by Green Functions Method? Could you give some hints?
$\ddot{x}_1(t)+a_1x_1(t)-a_2x_2(t)=f_1(t)$,
$\ddot{x}_2(t)+a_3x_2(t)-a_4x_1(t)=f_2(t)$,
where $a_1,a_2,a_3,a_4$ are constants.
The given conditions are as follows: ${x}_1(0)=k,{x}_2(0)=l,\dot{x}_1(0)=m,\dot{x}_2(0)=n$ where $k, l, m, n$ are constants.
($f_1(t),f_2(t)$ are ungiven functions.)
(You can find the transformed first order differential eq's. system of the second order system)