Find the Series Solution of the Differential Equation $y ^ { tt } - 7 x y ^ { t } = 0 \text { given the initial }$

Multiple Choice

Find the series solution of the differential equation $y ^ { tt } - 7 x y ^ { t } = 0 \text { given the initial }$ conditions $y ( 0 ) = 0$ and $y ^ { t } ( 0 ) = 4$

A) $y = 4 \left( 1 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n + 1 } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) } \right)$
B) $y = 4 \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) }$
C) $y = 4 \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n + 1 } x ^ { 2 n + 1 } } { 2 ^ { n } ( 2 n + 1 ) ! }$
D) $y = 4 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } ( 2 n + 1 ) ! }$
E) $y = 4 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) }$