3. (40) The differential equation 4xy" + 2y' + y = 0 has a regular singular point at x = 0. The Method of Frobenius assures the existence of at least one solution of the form y = >akaktr. *=0 a. (15) Find the indicial equation and its roots r] and r2, 71 2 72. b. (15) Find the recursion relation that determines ax+1 in terms of ax using the general value of r. c. (5) Using the larger root r1, and choosing ao = 1 for convenience, find the general coefficient ax in terms of k. Express the solution y corresponding to r, as the sum of a series using the preceding information. Is y1 an elementary function of a? d. (5) Now use the smaller root r2 and choose an = 1. Find ax in terms of k, and find a second solution y2. Write the general solution, expressing it if possible as an elementary function