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

Question 1

Multiple Choice

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


A) (k+2) (k+1) ck+2+ck=0( k + 2 ) ( k + 1 ) c _ { k + 2 } + c _ { k } = 0
B) (k+2) (k+1) ck+ck2=0( k + 2 ) ( k + 1 ) c _ { k } + c _ { k - 2 } = 0
C) (k+1) kck+2+ck=0( k + 1 ) k c _ { k + 2 } + c _ { k } = 0
D) (k+1) kck+ck2=0( k + 1 ) k c _ { k } + c _ { k - 2 } = 0
E) (k2) (k1) ck2+ck=0( k - 2 ) ( k - 1 ) c _ { k - 2 } + c _ { k } = 0

Correct Answer:

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