Consider This Second-Order Nonhomogeneous Differential Equation:

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

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