Taylor's Theorem to Find the First Four Terms of the Series

Multiple Choice

Taylor's Theorem to find the first four terms of the series solution of $y ^ { tt } + x ^ { 2 } y ^ { t } - ( \cos x ) y = 0$ given the initial conditions $y ( 0 ) = 7$ , and $y ^ {t } ( 0 ) = 4$

A) $y = 7 + \frac { 4 } { 1 ! } x + \frac { 7 } { 2 ! } x ^ { 2 } - \frac { 8 } { 3 ! } x ^ { 3 } + \cdots$
B) $y = 7 + \frac { 4 } { 1 ! } x + \frac { 7 } { 2 ! } x ^ { 2 } + \frac { 4 } { 3 ! } x ^ { 3 } + \cdots$
C) $y = 7 + \frac { 4 } { 1 ! } x + \frac { 14 } { 2 ! } x ^ { 2 } + \frac { 8 } { 3 ! } x ^ { 3 } + \cdots$
D) $y = 7 + \frac { 4 } { 1 ! } x + \frac { 4 } { 2 ! } x ^ { 2 } - \frac { 14 } { 3 ! } x ^ { 3 } + \cdots$
E) $y = 7 + \frac { 4 } { 1 ! } x + \frac { 4 } { 2 ! } x ^ { 2 } + \frac { 7 } { 3 ! } x ^ { 3 } + \cdots$