Hello! This is my first post in this forum, I spend mamy time in this exercise, but I can't iron out. Maybe someone help me? It's very important for me, because in september I need pass the exam.
Then you should not be attempting an equation like this. There are several different ways, involving reducing to a single second order equation or finding eigenvalues of a related matrix, but you seem to be saying you do not know those. Learn higher order linear differential equations before attempting systems of equations.