Consider This Second-Order Nonhomogeneous Differential Equation:

Which of the Following

Consider this second-order nonhomogeneous differential equation:

Which of the following is the form of the solution of the corresponding homogeneous differential equation? Here, C₁ and C₂ are arbitrary real constants

A) $Y(t) =A t \cos (3 t)$
B) $Y(t) =A t \cos (3 t) +B t \sin (3 t)$
C) $Y(t) =(A t+B) \sin (3 t) +(C t+D) \cos (3 t)$
D) $Y(t) =\left(A t^{2}+B t+C\right) \sin (3 t) +\left(D t^{2}+E t+F\right) \cos (3 t)$
E) $Y(t) =A t^{2} \cos (3 t) +B t^{2} \sin (3 t)$