1. The problem statement, all variables and given/known data x''(t)+r*x't+kx=0 Suppose that for some initial conditions the solution is given by x=e^(-2t)*(3cos(t)+4sin(t)) What are are and k? 2. Relevant equations See above 3. The attempt at a solution I've tried to "brute force" the solution simply by sticking the expression for x into the ODE, but that quickly becomes very complicated, and is easy to mess up. I can check my answers with wolfram alpha or some such, but it still will be difficult to pinpoint errors. Instead, I've heard that the values 3 and 4 don't matter (presumably they are determined by initial conditions, not r and k), and that there is a (relatively) simple expression that will make it easy to get the derivative and double derivative of this expression. I assume Euler's formula is involved somehow, but don't know exactly how to work it so that I can turn the entire function into an exponential.