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 $y ^ { \prime \prime } + 9 y = \sin ( 3 x )$ is

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