2. Consider the following initial value problem 6 (x - 1) 4 y 21 - 12 y 21 - 1:2 1 =0 , y(1) =0 , #'(1) =0 (a) Find an interval on which this IVP is guaranteed to have a unique solution (Use the E/U theorem). (b) Show that 1 is an ordinary point of the DE. Justify your answer by citing an appropriate definition or proposition from the Course Notes. (c) Consider the power series about 1 for pi(a) and po(a) are PI(T) = -6(x - 1)2+ , po(x) = -4(x - 1)20 1=0 71=0 use the Ratio Test (from Appendix A.1 of the course Note) to find the radius of convergence for these series. (d) To solve the DE using power series about 1, what is the guaranteed minimum radius of convergence of the resulting series? How does this compare with your answer from part a)