If a curve \( y=f(x) \) passes through the point \( (1,-1) \) and satisfies the differential equ....

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If a curve \( y=f(x) \) passes through the point \( (1,-1) \)
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and satisfies the differential equation, \( y(1+x y) d x= \)
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\( x d y \), then \( f\left(-\frac{1}{2}\right) \), is equal to
(1) \( -\frac{2}{5} \)
(2) \( -\frac{4}{5} \)
(3) \( \frac{2}{5} \)
(4) \( \frac{4}{5} \)


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