I have a system of linear differential equations with known boundary conditions. First of all what is the general solution to such a system? I know it is exponentials with the eigenvalues, but I couldn't find any place where the exact full solution was stated. Second of all, I want to write a program in matlab that solves this set of linear differential equations. In general how am I better off: - Simulate the solutions numerically starting from scratch i.e. dy1 dy2, dt and everything are numerical quantities - Find eigenvalues to the coefficient matrix numerically, plug into the analytical solution (which is the one I am not completely sure off, but I think you can write up a general formula) and solve for the unknown constants by applying boundary conditions.