I presume that if you are taking an exam in September, then you are taking the course now. Certainly, you must have learned something about problems like this. How would you solve a system of equations like this?
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.