Solve the Differential Equation $$10 y ^ { tt } - x y ^ { t } - y = 0$$

Multiple Choice

Solve the differential equation $$10 y ^ { tt } - x y ^ { t } - y = 0$$

A) $y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n } n ! }$ , where $a _ { 0 }$ is an arbitrary constant
B) $y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { ( n + 1 ) ! }$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
C) $y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { 10 ^ { n } \cdot 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
D) $y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n + 1 } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants
E) $y = a _ { 0 } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } \cdot 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }$ , where $a _ { 0 }$ and $a _ { 1 }$ are arbitrary constants