1. The problem statement, all variables and given/known data 1) Find the general solution of y''+ω02=Ccos3(ωx) 2) Show there exists two frequencies at which resonance occurs and determine them 3. The attempt at a solution I've tried the method of undetermined coefficients, assuming a solution of the form y=(Acos(ωx)+Bsin(ωx))3. I'm not 100% sure about this - if the RHS was just one trigonometric function, then you assume a solution that's a linear combination of sines and cosines. The trig function here is cubed so I just assumed you cube the linear combination. Is this correct the correct approach? Algebra is real hairy if it is! For the second part, what exactly is resonance in this context - what am I supposed to show?