Consider the First-Order Differential Equation $c_{1}=0, n c_{n+1}=7 c_{n-1}, n=1,2, \ldots$

Multiple Choice

Consider the first-order differential equation . - 7xy = 0.
Assume a solution of this equation can be represented as a power series .
What is the recurrence relation for the coefficients C_n ? Assume that C₀ is known.

A) $c_{1}=0, n c_{n+1}=7 c_{n-1}, n=1,2, \ldots$
B) $c_{0}=0,(n+1) c_{n}=7 c_{n-1}, n=1,2, \ldots$
C) $c_{0}=0,(n+1) c_{n+1}=7 c_{n-1}, n=1,2, \ldots$
D) $c_{0}=0,(n+1) c_{n+1}=7 c_{n}, n=0,1,2, \ldots$
E) $c_{1}=0,(n+1) c_{n+1}=7 c_{n-1}, n=1,2, \ldots$