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

Question 12

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 (for k=0,1,2,…k = 0,1,2 , \ldots )


A) (k+2) (k+1) ck+2=ck( k + 2 ) ( k + 1 ) c _ { k + 2 } = c _ { k }
B) (k+2) (k+1) ck=ck−2( k + 2 ) ( k + 1 ) c _ { k } = c _ { k - 2 }
C) (k+1) kck+2=ck( k + 1 ) k c _ { k + 2 } = c _ { k }
D) (k+1) kck=ck−2( k + 1 ) k c _ { k } = c _ { k - 2 }
E) (k−2) (k−1) ck−2=ck( k - 2 ) ( k - 1 ) c _ { k - 2 } = c _ { k }

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