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 $y ^ { \prime \prime } + 4 y ^ { \prime } + 5 y = e ^ { - 2 x } \cos x$ is

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