$\text { Solve the first-order linear differential equation } \frac { d y } { d x } = ( y - 1 ) \sin ( 2 x ) \text {. }$

Multiple Choice

$\text { Solve the first-order linear differential equation } \frac { d y } { d x } = ( y - 1 ) \sin ( 2 x ) \text {. }$

A) $y = 1 + C e ^ { \sin ( 2 x ) }$
B) $y = 1 + C e ^ -{ \frac { \cos ( 2 x ) } { 2 } }$
C) $y = 1 + C e ^ { \frac { \sin ( 2 x ) } { 2 } }$
D) $y = 1 + C e ^- { \frac { \sin ( 2 x ) } { 2 } }$
E) $y = 1 + C e ^ { \cos ( 2 x ) }$