Without Solving for the Undetermined Coefficients, the Correct Form of a Particular

Multiple Choice

Without solving for the undetermined coefficients, the correct form of a particular solution of the differential equation $y ^ { \prime \prime } + 6 y ^ { \prime } + 13 y = e ^ { - 3 x } \cos ( 2 x )$ is

A) $y _ { p } = A e ^ { - 3 x } \cos ( 2 x )$
B) $y _ { p } = A e ^ { - 3 x } \cos ( 2 x ) + B e ^ { - 3 x } \sin ( 2 x )$
C) $y _ { p } = A e ^ { 3 x } \cos ( 2 x )$
D) $y _ {p } = A x e ^ { - 3 x } \cos ( 2 x ) + B x e ^ { - 3 x } \sin ( 2 x )$
E) $y _ { p } = A x e ^ { - 3 x } \cos ( 2 x ) + B e ^ { - 3 x } \sin ( 2 x )$