Sorry, no. That's not allowed. If your matrix starts having operators in it, then finding the eigenvalues (which is ultimately what you're trying to do) becomes very much more complicated. Ph.D. theses have been written on that sort of thing (mine was!).

Your problem looks like a circuit problem. So you have a system of ODE's, correct? How are you expecting to solve it without having n equations? Perhaps you could post the original problem here, or is that the original problem?