Solve the differential equation using power series

Question

If the series y(x) = Σn=0 to infinity (Cn x^n) is a solution of the differential equation 3y''-3x^2y'+3y=0. A general solution of the same equation can be written as y(x) = C0y1(x) + C1y2(x), where:

y1(x) = 1+Σn=2 to infinity (an x^n), y2(x) = x+Σn=2 to infinity (bn x^n)

find: a2,a3,a4,b2,b3,b4

Answer 1

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