1. The problem statement, all variables and given/known data Find two non-zero terms of the power series solution of y' = 1 + y^2 ,y(0) = 0 by using series substitution y(x) = sum (k=0 to inf) [a][/k] *x^k 2. Relevant equations 3. The attempt at a solution First take the derivative of the power series to get y' = sum (k=0 to inf) (k+1)*[a][/k+1]*x^k Plug y and y' into the original ODE, here is where my problem is. I want the powers of x to match so that i can match the coefficients of the series and get a recursive relationship to find the non-zero terms. How do i deal with the y^2 term? How do I square a series and still get matching x-terms?