The Recurrence Relation for the Differential Equation $2 x y ^ { \prime \prime } - y ^ { t } + 2 y = 0$

Multiple Choice

The recurrence relation for the differential equation $2 x y ^ { \prime \prime } - y ^ { t } + 2 y = 0$ is

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