If `xdy = y(dx + ydy); y(1) = 1 and y(x) > 0`, then what is `y(-3)` equal to?

Options

A. 3
B. 2
C. 1
D. 0

Answer

a

Explanation

Given , `xdy = y (dx + ydy), y gt 0`
` rArr xdy - ydx = y^(2)dy `
` rArr (xdy-ydx)/(y^(2)) = dy rArr d(x/y) = -dy`
On integrating both sides , we get
` x/y = -y +C " "` …(i)
Since , ` y (1) =1 rArr x = 1 , y =1`
` :. C = 2`
Now , Eq, (i) becomes
Again for x=-3
rArr ` -3 +y^(2) = 2Y`
` rArr y^(2) - 2y - 3 = 0`
` rArr (y+1)(y-3)=0`
As `y gt 0` take y = 3 , neglecting y = -1