1. The problem statement, all variables and given/known data Find the indicated coefficients of the power series solution about x = 0 of the differential equation: y'' - (sinx)y = cosx, y(0) = -5, y'(0) = 3. y = _ + _x + _x^2 + _x^3 + _x^4 + O(x^5) 2. Relevant equations 3. The attempt at a solution This is going to be a tad confusing in typing it, but I hope it can be read. I have the summation(anx^n) This equals y. y' = summation(nanx^n-1) y'' = summation (n(n-1)anx^n-2) Just to make it easier, we end up with x^n[(n+2)(n+1)an+2-ansinx] = cosx Thus, an+2 = (cosx + ansinx) / ((n+2)(n+1)) I know obviously that the first two terms (x^0 and x^1) are -5 and 3 respectively. I also know that the x^2 term is 0.5 by plugging in 0 for x. However, this doesn't work for the rest of them. I've done a lot of these types of problems, but this is the first one with sin(x) or cos(x), which puts an "x" in the an+2 equation (which I wrote above). What does x equal in this case? Can anyone just show me how to find the remaining coefficients because I'm pretty sure my equation is correct.