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

xdy = ydx ` + y^(2)dy`
` Rightarrow x.(dy)/(dx) =y +y^(2) .(dy)/(dx) Rightarrow (y -x.(dy)/(dx))/(y^(2)) = (-dy)/(dx)`
Integrating both sides
` x/y =-y +c`
Given x=1,y =1
`Rightarrow 1/1 = -1 +c Rightarrow c =2`
`x/y +y=2`
` Rightarrow x+y^(2) =2y`
` Rightarrow -3 + y^(2) -2y =0`
` Rightarrow y^(2) -2y -3=0`
y =3,-1
y=3