Solve the following second-order linear difference equations:

(a) xn+2 = 5xn+1 − 6xn, n = 0, 1, 2, 3, . . . , if x0 = 1, x1 = 4;

(b) xn+2 = xn+1 − 1 4xn, n = 0, 1, 2, 3, . . . , if x0 = 1, x1 = 2;

(c) xn+2 = 2xn+1 − 2xn, n = 0, 1, 2, 3, . . . , if x0 = 1, x1 = 2;

(d) Fn+2 = Fn+1 + Fn, n = 0, 1, 2, 3, . . . , if F1 = 1 and F2 = 1 (the sequence of numbers is known as the Fibonacci sequence);

(e) xn+2 = xn+1 + 2xn − f (n), n = 0, 1, 2, . . . , given that x0 = 2 and x1 = 3, when (i) f (n) = 2, (ii) f (n) = 2n, and (iii) f (n) = en (use Mathematica for part (iii) only).