Using Taylor Series About C = 1, the General Series $y ^ { \prime } + 2 ( x - 1 ) y = 0$

Multiple Choice

Using Taylor series about c = 1, the general series solution, with the first three nonzero terms, of the differential equation $y ^ { \prime } + 2 ( x - 1 ) y = 0$ is

A) $y = A \left( 1 + ( x - 1 ) ^ { 2 } - \frac { ( x - 1 ) ^ { 4 } } { 2 } - \frac { ( x - 1 ) ^ { 6 } } { 6 } + \cdots \right)$
B) $y = A \left( 1 - ( x - 1 ) ^ { 2 } + \frac { ( x - 1 ) ^ { 4 } } { 2 } - \frac { ( x - 1 ) ^ { 6 } } { 6 } - \cdots \right)$
C) $y = A \left( 1 - ( x - 1 ) ^ { 2 } - \frac { ( x - 1 ) ^ { 4 } } { 2 } - \frac { ( x - 1 ) ^ { 6 } } { 6 } - \cdots \right)$
D) $y = A \left( 1 - ( x - 1 ) ^ { 2 } + \frac { ( x - 1 ) ^ { 4 } } { 2 } - \frac { ( x - 1 ) ^ { 6 } } { 6 } + \cdots \right)$
E) $y = A \left( 1 + ( x - 1 ) ^ { 2 } + \frac { ( x - 1 ) ^ { 4 } } { 2 } + \frac { ( x - 1 ) ^ { 6 } } { 6 } + \cdots \right)$