The differential equation obtained by eliminating the arbitrary constant a and b from $xy=ae^x+be^{-x}$ is

$\begin {array} {1 1} (a)\;x \frac{d^2 y}{dx^2}+2 \frac{dy}{dx}-xy=0 & \quad (b)\; \frac{d^2 y}{dx^2}+2y \frac{dy}{dx}-xy = 0 \\ (c)\;x \frac{d^2 y}{dx^2} + 2 \frac{dy}{dx}+xy=0 & \quad (d)\; \frac{d^2 y}{dx^2}+ \frac{dy}{dx}-xy=0 \end {array}$

$(a)\;x \frac{d^2 y}{dx^2}+2 \frac{dy}{dx}-xy=0$