The Correct Form of the Particular Solution Of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$

Multiple Choice

The correct form of the particular solution of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$ is

A) $y _ { p } = A e ^ { - x }$
B) $y _ { p } = A x e ^ { - x }$
C) $y _ { p } = A x ^ { 2 } e ^ { - x }$
D) $y _ { p } = A x ^ { 3 } e ^ { - x }$
E) none of the above