plz show the step by step solution, thankkks

4x2y" + (x2 +.1|:)yr y = 0. (a) Without solving this differential equation, one can say that any power series solution centered at the ordinary point x9 = 2 (i.e. a series involving powers of x 2) has a radius of convergence at least equal to R. What is R? (Enter infinity if]? = 00.) (1)) Find the two roots of the indicial equation associated with the regular singular point x0 = 0. Separate your answers with a comma. (c) If r1 denotes the largest of the 2 roots of the indicial equation, the differential equation above has a solution of the form on 2 C" xn+r1 n=0 where on = g(n)c"_1, n 2 l, for a certain function g(n). Compute 3(a). (d) Write the sum of the rst 3 non-zero terms of the series in (c) if Ct] = l. (e) What is the radius of convergence of the series in (c) if 0.0 = 1? (Enter infinity if it is innite.)