The General Solution of the First-Order Differential Equation $x y ^ { \prime } + ( 1 + x ) y = e ^ { x }$

Multiple Choice

The general solution of the first-order differential equation $x y ^ { \prime } + ( 1 + x ) y = e ^ { x }$ is

A) $4 x y = e ^ { x } + C e ^ { - x }$
B) $3 x y = e ^ { x } - C e ^ { - x }$
C) $3 x y = e ^ { x } + C e ^ { - x }$
D) $2 x y = e ^ { x } - C e ^ { - x }$
E) $2 x y = e ^ { x } + C e ^ { - x }$