## Finding the solution of Un and Vn

Show that if $U_n and V_n$ are solutions of $\Delta^{2} y_{n} + p_{n} \Delta y_{n}+ q_{n}y_{n} = 0$ and $C_{n}=$ $\left(\begin{array}{cc}U_{n}&Y_{n}\\ \Delta U_{n}&\Delta Y_n \end{array}\right)$, then $\Delta C_{n} + (p_{n} - q_{n})C_{n} = 0$