Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=A e^{8 t}\left[\sin \frac{\pi}{9} t+\cos \frac{\pi}{9} t\right]+B$

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 to be used? Here, all capital letters represent arbitrary real constants.

A) $Y(t) =A e^{8 t}\left[\sin \frac{\pi}{9} t+\cos \frac{\pi}{9} t\right]+B$
B) $Y(t) =A e^{8 t} \sin \left(\frac{\pi}{9} t\right) +B$
C) $Y(t) =e^{A t}(\sin (B t) +\cos (B t) )$
D) $Y(t) =A e^{8 t} \sin \left(\frac{\pi}{9} t\right)$
E) $Y(t) =e^{8 t}\left(A \sin \frac{\pi}{9} t+B \cos \frac{\pi}{9} t\right)$