# How to solve a system of differential equations

When I solved one problem, I faced with the need to solve the following system of differential equations:

1) $\ddot{x}(t)-a(t)x(t)-b(t)y(t)-c(t)=0$

2) $\ddot{y}(t)-d(t)y(t)-b(t)x(t)-e(t)=0$

Here $x$, $y$-functions of time: $x=x(t)$, $y=y(t)$;

And $a(t)$, $b(t)$, $c(t)$, $d(t)$, $e(t)$ are known functions of $\cos(\omega t)$, $\sin(\omega t)$ (here $\omega$-constant).

So, I want to find $x(t)$, $y(t)$. Can you help me?

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