Suppose a Ninth-Order Homogeneous Linear Differential Equation with Constant Coefficients $C t \sin (6 t)$

Multiple Choice

Suppose a ninth-order homogeneous linear differential equation with constant coefficients has these characteristic roots: -6i, -6i, 6i, 6i, , - , - , -6.2
Which of the following terms are part of the general solution of this equation? Here, C denotes an arbitrary real constant.Select all that apply.

A) $C t \sin (6 t)$
B) $\mathrm{Ct}$
C) $\mathrm{C}$
D) $C \sqrt{11}$
E) $C t^{2} e^{-\sqrt{11} t}$
F) $C e^{\sqrt{11} t} \cos (6 t)$
G) $C t^{2} \cos (6 t)$
H) $\mathrm{Ce}-\sqrt{11} t$