A Particular Solution of the Differential Equation $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$

Multiple Choice

A particular solution of the differential equation $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$ is

A) $y _ { p } = x ^ { 2 } e ^ { - x } / 2$
B) $y _ { p } = x e ^ { - x } / 2$
C) $y _ { p } = x e ^ { - x }$
D) $y _ { p } = e ^ { - x }$
E) $y _ { p } = e ^ { - x } / 4$