Differential equations

Solve the system of differential equations

 \ddot y_1 = y_2-2y_1-\Gamma \dot y_1 + F_1 e^{\imath \omega t} \\ \ddot y_2 = y_3-3y_2+y_1-\Gamma \dot y_2 \\ \ddot y_3 = -2y_3+y_2-\Gamma \dot y_3 + F_3e^{\imath \omega t}

where y_i = y_i(t).