What Is the Form of a Particular Solution of the Following

Multiple Choice

What is the form of a particular solution of the following nonhomogeneous differential equation?

All capital letters in the choices represent arbitrary real constants.

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