I'm doing research as a grad student and I'm stuck on solving a system of differential equations, with a periodic matrix:
$\dot{x}=\begin{bmatrix}a-\cos(t)& b\\b &a+\cos(t) \end{bmatrix}x$
Is there a way to find solutions for $x(t)$ ?
In my readings, I found Floquet theory might be useful, but I can't make enough sense of it to apply it to my problem.
Also, the following link might be useful, though I couldn't make it work here: Decoupling coupled differential equations with time dependent coefficients.