Consider the following differential equation, 5xy" + (1+x) y' + 2y: = 0. Note that xo = 0 is a regular singular point. Suppose that we look for a series solution of the form y = Σcnxn+r. n=0 (a) Find the two roots of the indicial equation. (b) The recurrence formula for the coefficients of the solution with the larger root is given by Ck+1 = g(k) ck, k ≥ 0. Enter the function g(k) into the answer box below. (c) Taking co = 1, find the first 3 terms of the solution corresponding to the largest root.

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