Discuss about green function approach

Question

Problem:Important information about Green's Function

Consider the nonhomogeneous linear initial value problem

x²yⁿ - 2xy' + 2y = 30xδ(x - 3), y(1) = 1, y'(1) = 0

Note that y(x) = x satisfies the corresponding homogeneous differential equation. Solve the initial problem using a Green's function approach. What happens to y, y' and yⁿ at x=3?