# Finding the general solution with nontrivial solutions

Consider the differental equation $y_{n+2} + a_n y_n= 0, a_n does not equal zero$. Let Un and Vn be nontrivial solutions of the D.E. Let $C_n = \left(\begin{array}{cc}U_n&V_n\\u_{n+1}&v_{n+1}\en d{array}\right)$. Show that $C_{n+1} = a_n C_n$ and write out the general solution of $C_{n+1} = a_n C_n$ since this equation is first order and linear.