A Particular Solution of the Differential Equation $y ^ { \prime \prime } + 3 y ^ { \prime } - 4 y = e ^ { x }$

Multiple Choice

A particular solution of the differential equation $y ^ { \prime \prime } + 3 y ^ { \prime } - 4 y = e ^ { x }$ is

A) $y _ { p } = x ^ { 2 } e ^ { x }$
B) $y _ { p } = x e ^ { x } / 5$
C) $y _ { p } = x e ^ { x }$
D) $y _ { p } = e ^ { x }$
E) $y _ { p } = e ^ { - x } / 5$