If a curve y = f x passes through the point ( 1 , - 1 ) and satisfies the differential equation, y   1…

If a curve y=fx passes through the point (1,-1) and satisfies the differential equation, y 1+xydx=x dy, then f-12 is equal to
  1. 25
  2. 45
  3. -25
  4. -45

Solution

Given differential equation,

ydx+xy2dx=xdy

⇒ xdy-ydxy2=xdx

⇒ -dxy=dx22

On integrating we get,

⇒-xy=x22+C

∵ It passes through (1,-1).

∴ 1=12+C ⇒  C=12

∴ x2+1+2xy=0  ⇒  y=-2xx2+1

∴ f-12=45

Asked in: JEE Main 2016 (03 Apr)

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