Answer
(a) $3\cos x$ is not a solution.
(b) $3\cos 2x$ is a solution.
(c) $e^{-2x}$ is a solution.
(d) $3 e^{2x}-4 \sin 2x $ is a solution.
Work Step by Step
Consider the linear differential equation $y^{(4)}-16 y=0$
(a) $3\cos x$ is not a solution.
(b) $3\cos 2x$ is a solution.
(c) $e^{-2x}$ is a solution.
(d) $3 e^{2x}-4 \sin 2x $ is a solution.