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

question 12

Multiple Choice

The recurrence relation for the power series solution about $x = 0$ of the differential equation $y ^ { \prime \prime } - y = 0$ is (for $k = 0,1,2 , \ldots$ )

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