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

Multiple Choice

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

A) $y _ { p } = A x + B + C e ^ { x }$
B) $y _ { p } = \left( A x + B + C e ^ { x } \right) x$
C) $y _ { p } = A x ^ { 2 } + B + C e ^ { x }$
D) $y _ { p } = A x ^ { 2 } + B x + C e ^ { x }$
E) $y _ { p } = A x + B + C x e ^ { x }$