Assume a series solution x(t) =summation ^ infinity _ n = 0 a_n t ^n for the equation x" + x = 0. show that the recursion formula for the coefficients is a_m + 2= -a _m/(m + l1(m + 2), m = 0, 1, and that this leads to the general solution x (t) = a_0 (1 - t^2/2! + t^4/4! + +a_1 (t - t^3/3! + t^5/5! + = a_0 cos(t) + a_1 sin(t)