If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation,$y(1 + xy) dx = x dy,$ then $f\bigg(\large\frac{-1}{2}\bigg)$ is equal to :

Question

$\begin{array}{1 1}(1)\large\frac{2}{5} \\ (2)\large\frac{-4}{5} \\(3) \large\frac{2}{5} \\ (4)\large\frac{4}{5} \end{array} $