Mathematics

Problem

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\left(-\frac{1}{2}\right)

is equal to : (1)

-\frac{2}{5}

(2)

-\frac{4}{5}

(3)

\frac{2}{5}

(4)

\frac{4}{5}