3) Consider a series solution for the equation xy" - 2y' + xy=0 a) Show that the indicial equations has two roots that differ by an integer but that never- theless the two roots generate linearly independent solutions: Y₁(x) = 3a0 (-1)+12x2n+1 (2n+1)! n=1 42(x) = 40 Σ n=0 (-1)+1 (2n-1)x2n (2n)! b) Show that y(x) = 3a0(sin x-x cos x) by expanding the sinusoidal functions. Then use the Wronskian method to find y2(x) in terms of sinusoidal functions. c) Confirm that the two solutions are linearly independent.