Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=A e^{5 t}+B \cos (7 t)$

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) $Y(t) =A e^{5 t}+B \cos (7 t)$
B) $Y(t) =(A t+B) e^{5 t}+(C t+D) \cos (7 t)$
C) $Y(t) =A e^{5 t}+B \cos (7 t) +C \sin (7 t)$
D) $Y(t) =(A t+B) e^{5 t} \cos (7 t) +(C t+D) e^{5 t} \sin (7 t)$