Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 2 / 1A / Solution

The homogeneous linear recurrence relationhas characteristic polynomial $(r-2{)}^2$, soFor a particular solution, substitute $y_n=an+b$. The left-hand side becomesso matching $n$ gives $a=1$ and $b=2$. HenceThe conditions $y_0=1$ and $y_1=0$ give $C=-1$ and $D=-1/2$. Therefore