So I'm curious how to actually find Floquet multipliers given some differential equation y'=A(t)y. It's (usually) easy to find the fundamental matrix $\Phi(t)$ by other methods. And I feel like I'm missing something dumb, but what can I do from there to get the eigenvalues for the matrix $C$?
For a more concrete example at hand, consider y'=(a+b\cos t)y. It is easy to see that $y=(C_0e^{at})e^{b\sin t}$ and the period of the periodic matrix is $p=2\pi$. So now I have: $\Phi(t+p)C=\Phi(t)\implies(C_0e^{A(t+2\pi)})e^{B\sin{(t+2\pi)}}C=(C_0e^{At})e^{B\sin{t}}$ How do I get $C$, or more specifically, the eigenvalues of C once I have this setup? I'm pretty sure I did something incorrectly.
EDIT: Sorry, figured it out with anon's help. I completely mixed up my notions for computing the fundamental matrix.