(i) Find the general solution of the difference equation

$$u_{k+1}+5 u_{k}+6 u_{k-1}=12 k+1$$

(ii) Find the solution of the equation

$$y_{k+1}+5 y_{k}+6 y_{k-1}=2^{k}$$

that satisfies $y_{0}=y_{1}=1$. Hence show that, for any positive integer $n$, the quantity $2^{n}-26(-3)^{n}$ is divisible by $10 .$