(a) Find a solution that is not identically zero, of the homogeneous linear differential equation (3x2−x−1)y′′−(9x2+9x−2)y′+(18x+3)y=0. Intelligent guessing of the form of a solution may be helpful.
(b) Let y=f(x) be the solution of the nonhomogeneous differential equation (3x2−x−1)y′′−(9x2+9x−2)y′+(18x+3)y=6(6x+1) that has f(0)=1 and (f(−1)−2)(f(1)−6)=1. Find integers a,b,c such that (f(−2)−a)(f(2)−b)=c.