Consider the Second-Order Differential Equation + 64y = 0 $c_{n+2}+64 c_{n}=0, n=0,1,2, \ldots$

Multiple Choice

Consider the second-order differential equation + 64y = 0.
Assume a solution of this equation can be represented as a power series
What is the recurrence relation for the coefficientsC_n ? Assume that C₀ and C₁ are known.

A) $c_{n+2}+64 c_{n}=0, n=0,1,2, \ldots$
B) $c_{n+1}+64 c_{n}=0, n=0,1,2, \ldots$
C) $(n+1) (n+2) c_{n+2}+64 c_{n}=0, n=0,1,2, \ldots$
D) $n(n+1) c_{n+1}+64 c_{n}=0, n=0,1,2, \ldots$