1. The problem statement, all variables and given/known data Solve y''+(cosx)y=0 with power series (centered at 0) 2. Relevant equations y(x) = Σ anxn 3. The attempt at a solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...) =a0+a1x+(a2-a0/2)x2+(a3-a1/2)x3+... Then I computed y'' as follows: y'' = 2a2+6a3x+12a4x2+... I assembled everything (y''+ycosx = 0): (a0+2a2)+(6a3+a1)x+(12a4+a2-a0/2)x2+... = 0 Finally I computed the constants: a0+2a2=0 => a2=-a0/2 6a3+a1=0 => a3=-a1/6 12a4+a2-a0/2)x2=0 => a4=a0/12 ... and so on for a couple of more terms. My final answer is then: y(x) = a0(1-x2/2+x4/12-x6/80+...)+a1(x-x3/6+x5/30+...) Does this make sense? Is there a 'less-messy' way of doing this?