Find the First Six Terms of the Power Series Representing $\left( x ^ { 2 } + 2 \right) y ^ { tt } + y = 0$

Find the first six terms of the power series representing independent solutions of the differential equation $\left( x ^ { 2 } + 2 \right) y ^ { tt } + y = 0$ .

A) $y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 4 } - \frac { x ^ { 4 } } { 32 } - \cdots \right) + a _ { 1 } \left( x - \frac { x ^ { 3 } } { 12 } - \frac { 7 x ^ { 5 } } { 480 } - \cdots \right)$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
B) $y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 4 } + \frac { x ^ { 4 } } { 96 } - \cdots \right) + a _ { 1 } \left( x - \frac { x ^ { 3 } } { 12 } + \frac { 7 x ^ { 5 } } { 480 } - \cdots \right)$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
C) $y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 4 } + \frac { x ^ { 4 } } { 32 } - \cdots \right) + a _ { 1 } \left( x - \frac { x ^ { 3 } } { 12 } + \frac { 7 x ^ { 5 } } { 480 } - \cdots \right)$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
D) $y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 8 } - \cdots \right) + a _ { 1 } \left( x - \frac { x ^ { 3 } } { 6 } + \frac { 7 x ^ { 5 } } { 120 } - \cdots \right)$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
E) $y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 4 } + \frac { x ^ { 4 } } { 16 } - \cdots \right) + a _ { 1 } \left( x - \frac { x ^ { 3 } } { 12 } + \frac { 7 x ^ { 5 } } { 240 } - \cdots \right)$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants