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