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Find Recursive Relation for Coefficients of Power Series

MVCALC-4CALWD

Find the recursive relation for the coefficients of the power series solution centered at $x_0 = 0$ to:

$$y'' - y= 0$$

A

$(n+2)(n+1) a_{n+2} - a_n = 0$ for $n = 0,1,2,\ldots$

B

$(n^2 - n - 1) a_n = a_{n+1}$ for $n = 0,1,2,\ldots$

C

$a_n = 0$ for $n = 0,1,2,\ldots$

D

$n(n-1) a_{n} = a_{n+2}$ for $n = 0,1,2,\ldots$

E

None of the Above