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If x dy =y (dx+y dy), y(1) =1and Y(x)gt ...

If `x dy =y (dx+y dy), y(1) =1`and `Y(x)gt 0`. Then, `y (-3) is epual to (a) 3 (b) 2 (c) 1 (d) 0

A

(a) 3

B

(b) 2

C

(c) 1

D

(d) 0

Text Solution

Verified by Experts

Given, `x dy =y(dx+ y dy),y gt 0`
`rArr x dy-ydx=y^(2)dy`
`rArr (x dy-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`
`therefore c=2`
Now, Eq. (i) becomes , `x/y +y =2`
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.
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