Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=A t \cos (3 t)$

Multiple Choice

Consider this second-order nonhomogeneous differential equation:

Which of these is a suitable form of a particular solution Y(t) of the nonhomogeneous differential equation if the method of undetermined coefficients is used? Here, all capital letters represent arbitrary real constants.

A) $Y(t) =A t \cos (3 t)$
B) $Y(t) =A t \cos (3 t) +B t \sin (3 t)$
C) $Y(t) =(A t+B) \sin (3 t) +(C t+D) \cos (3 t)$
D) $Y(t) =\left(A t^{2}+B t+C\right) \sin (3 t) +\left(D t^{2}+E t+F\right) \cos (3 t)$
E) $Y(t) =A t^{2} \cos (3 t) +B t^{2} \sin (3 t)$