### Differential equations

Solve the system of differential equations

$\ddot x + a_1\dot x + b_1\dot y + c_1 x + d_1 y = k_1 e^{\imath \omega t} \\ \ddot y + a_2\dot x + b_2\dot y + c_2 x + d_2 y = k_2 e^{\imath \omega t}$

where $x = x(t),\ \ \ y=y(t)$.