Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=A t^{2}+B t+C+D e^{-\sqrt{3} t}$

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) $Y(t) =A t^{2}+B t+C+D e^{-\sqrt{3} t}$
B) $Y(t) =\left(A t^{2}+B t\right) e^{-\sqrt{3} t}$
C) $Y(t) =A t(B t+3) e^{-\sqrt{3} t}$
D) $Y(t) =\left(A t^{2}+B t+C\right) e^{-\sqrt{3} t}$