Use Power Series to Solve the Differential Equation $y ^ { \prime \prime } - x y ^ { \prime } - y = 0 , y ( 0 ) = 7 , y ^ { \prime } ( 0 ) = 0$

Multiple Choice

Use power series to solve the differential equation. $y ^ { \prime \prime } - x y ^ { \prime } - y = 0 , y ( 0 ) = 7 , y ^ { \prime } ( 0 ) = 0$

A) $y ( x ) = 7 e ^ { x }$
B) $y ( x ) = 7 e ^ { - \frac { x ^ { 2 } } { 2 } }$
C) $y ( x ) = e ^ { 7 x }$
D) $y ( x ) = c e ^ { \frac { x ^ { 2 } } { 2 } }$
E) $y ( x ) = 7 e ^ { \frac { x ^ { 2 } } { 2 } }$