IF x dy `= y ( dx + y dy ) , y(1) = 1 ` and y `( x) gt 0` then `y(-3)` is equal to :

Options

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

Answer

A

Explanation

We have,
`xdy=y(dx+ydy)`
`rArr" "xdy-ydx=y^(2)dyrArr-((ydx-xdy)/(y^(2)))=dyrArr-d((x)/(y))=dy`
On integrating, we get
`(-x)/(y)=y+C`
It is given that y(1) = 1 i.e. y = 1 when x = 1
`therefore" "C=-2` in (i), we get `(-x)/(y)=y-2`
Putting x = `-3`, we get
`(3)/(y)=y-2`
`rArr" "y^(2)-2y-3=0rArr(y-3)(y+1)=0rArry=3" "[becauseygt0]`