I wan to solve the following ODE's:- $$L_1 q''(t)+R_1q'(t)+\frac 1C_1 q(t)-Mq_2''(t)=V\sin(\omega t)$$ $$L_2 q_2''(t)+R_2q_2'(t)+\frac 1C_2 q_2(t)-Mq''(t)=V\sin(\omega t)$$ $L,C,R,V>0$, I already know how to solve linear non-homogenous and non-coupled ODE, using the homogenous solution plus the particular solution found by using a trial function.
How can I reduce the given equations to non=coupled form so as to apply similar methodologies to solve them?
I just know the basic methods to solve simple ODE's.
I am comfortable with solving simple coupled ODE such as
$$y_1'(t)=Ay_2(t)\text{ and } y_2'(t)=B+Cy_1(t)$$
by simple substitution.
(The physics tag is added because these equations describe the behaviour of coupled RLC circuit with an application in metal detectors)