The solution of the differential equation y d x - x + 2 y 2 d y = 0 is x = f y . If f - 1 = 1 , then f ( 1 )…

The solution of the differential equation ydx-x+2y2dy=0 is x=fy. If f-1=1, then f(1) is equal to
  1. 2
  2. 3
  3. 4
  4. 1

Solution

ydx-xdy=2y2dy

ydx-xdyy2=2dy

dxy=2dy

∫dxy=2∫dy

xy=2y+c

x=2y2+cy

If y= -1, x=1

1=2-c

c=1

∴ Curve would be

x=2y2+y

If y=1 then x=3 .

Asked in: JEE Main 2015 (11 Apr Online)

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