QJEEM16Mab00b: JEE Main 2016 Mathematics - Class 12 JEEM16Mab00b Solution: If a curve y = f ( x ) passes through the point ( 1 , − 1 ) and …

Question

Verified Solution • 2025–26 Session moderate

If a curve

y = f (x)

passes through the point

(1, - 1)

and satisfies the differential equation,

y (1 + x y) d x = x

d y

, then

f (- \frac{1}{2})

is equal to :

Accepted Answer

y (1 + x y) d x = x d y

\frac{x d y - y d x}{y^{2}} = x d x \Rightarrow \int - d (\frac{x}{y}) = \int x d x

- \frac{x}{y} = \frac{x^{2}}{2} + C

as

y (1) = - 1 \Rightarrow C = \frac{1}{2}

Hence,

y = \frac{- 2 x}{x^{2} + 1} \Rightarrow f (\frac{- 1}{2}) = \frac{4}{5}

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