The Recurrence Relation for the Power Series Solution About $x = 0$

The recurrence relation for the power series solution about $x = 0$ of the differential equation $y ^ { \prime \prime } + y = 0$ is

A) $( k + 2 ) ( k + 1 ) c _ { k + 2 } + c _ { k } = 0$
B) $( k + 2 ) ( k + 1 ) c _ { k } + c _ { k - 2 } = 0$
C) $( k + 1 ) k c _ { k + 2 } + c _ { k } = 0$
D) $( k + 1 ) k c _ { k } + c _ { k - 2 } = 0$
E) $( k - 2 ) ( k - 1 ) c _ { k - 2 } + c _ { k } = 0$

Correct Answer:

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