The characteristic polynomial is \(x^2 - 6x + 9\text{.}\) We solve the characteristic equation
by factoring:
so \(x =3\) is the only characteristic root. Therefore we know that the solution to the recurrence relation has the form
for some constants \(a\) and \(b\text{.}\) Now use the initial conditions:
Since \(a = 1\text{,}\) we find that \(b = \frac{1}{3}\text{.}\) Therefore the solution to the recurrence relation is