Please help me solve this using the power series method..(Thinking)
Consider the differential eqaution
(1-x^2)y'' - 2xy' + a(a+1)y = 0
Where a is a constant. Find solutions y_1, y_2 for the DE such that 1) each of them is the sum of a convergent power series centered at the origin and 2) y_1 and y_2 are independent lie in c_1y_1 + c_2y_2 = 0 (c_1 and c_2 are zero). Prove y_1 and y_2 are independent. If a=4 show that the DE has a polynomial solution.
thanks in advance..