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

Question

( A ) $\frac{2}{5}$
( B ) $\frac{4}{5}$
( C ) $-\frac{2}{5}$
( D ) $-\frac{4}{5}$