For the differential equation: (2−x^2)y′′ − xy′ + x^2y = 0

(a) Compute the recursion formula for the coefficients of the power series solution centered at x0 = 0 and use it to compute the first three nonzero terms of the solution with y(0) = 0, y′(0) = −36.

(b) Show that the solution given in (a) is an odd function (Hint: what is an when n is even ?)