This kind of problem is just routine knowing the correspoonding theory. The solutions of the characteristic equation $\displaystyle \lambda^2-2\lambda -3=0$ are $\displaystyle \lambda=3,\;\lambda=-1$ so, the genearl solution is $\displaystyle x_k=C_13^k+C_2(-1)^k$. Now, use the initial conditions to determine $\displaystyle C_1$ and $\displaystyle C_2$.
Fernando Revilla