Hi, Could you please help me solve.

(a) Use a power series to obtain the general solution of the ODE y\" + 33/ + 2y 2 0. Identify the solution in terms of explicit functions. i.e. Identify the power series as known functions. (b) Consider the ODE 3x2y" + 2my' + (:1: 2)y = 0. (i) Look for a solution of the form 3/ = x3: aux\". Show that n=0 we must have s = 1 or s = 2/3. (ii) Show that the coefcients satisfy _a"n,1 an: (n+s)(3n+331)2' (iii) Use the recurrence relation for an to generate two linearly independent solutions for the ODE