I have a system of 2 coupled second order linear ordinary differential equations. Suppose we have $A(t) X'' + B(t) X' + C(t) X = 0$ with $A,B,C$ are $2 \times 2$ time dependent matrices.
I need to know, under fairly general conditions, when it is possible to diagonalize the system to uncouple the two degrees of freedom.
Any resources will be appreciated.