For $y=xe^x$, which of the following is correct ?

$x\frac{d^2y}{dx^2}-x\frac{dy}{dx}-y=0$ $x\frac{d^2y}{dx^2}-y\frac{dy}{dx}-x=0$ $x\frac{d^2y}{dx^2}+x\frac{dy}{dx}+y=0$ $y\frac{d^2y}{dx^2}-y\frac{dy}{dx}-x=0$

$x\frac{d^2y}{dx^2}-x\frac{dy}{dx}-y=0$