Consider the following differential equation, 5xy" +(1+x) y² + 2y = 0. Note that x = 0 is a regular singular point. Suppose that we look for a series solution of the form y - Σnt tr - La 7===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 +1 = g(k), k≥ 0. Enter the function g() into the answer box below. (c) Taking co = 1, find the first 3 terms of the solution corresponding to the largest root. Two roots, separated with a comma. Enter your answer as a symbolic function of k, as in these examples Enter your answer as a symbolic function of x, as in these examples

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