Consider the following equation: 2xy'' + y' + 3y = 0.
(a) Show that x0 = 0 is a regular singular point.
(b) Write down the indicial equation and solve it to determine r1 and r2, r1 ≥ r2.
(c) Let y= n=0Σ∞ cn (r) xn+r. Determine the recursive relation for cn(r), i.e., relation between cn+1(r) and cn(r).
(d) Take c0(r) = 1. Find two linearly independent solutions y1 and y2 which are valid for x>0 near x0 =0.