Find the recurrence relation for the coefficients of the power series solution of the differential equation y" + y' - 2y = 0 Assume the form y(x) = Sigma^infinity _n = 0 c_nx^n. First compute y'(x) = Sigma^infinity _n = 1 c_nx^n-1 = Sigma^infinity _n = 0 c_n + 1^x^n Then compute y"(x) = Sigma^infinity _n = 1 c_n + 1 x^n - 1 = Sigma^infinity _n = 0 c_n _ 2x^n Then y" + y' - 2u = Sigma^infinity _n = 0 [c_n + 2 + c_n + 1 + c_n]x^n Requiring that the terms of this series for y" + y' - 2y vanish gives the recurrence relation c_n = 2 = c_n + 1 + c_n for n = 0, 1, 2, ...