Question

If $x d y=y(d x+y d y), y(1)=1$ and $y(x)>0$, then $y(-3)$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

Given,
$\frac{x d y-y d x}{y^2}=d y \Rightarrow d\left(\frac{x}{y}\right)=-d y \Rightarrow \frac{x}{y}=-y+C$
As, $ y (1)=1 \Rightarrow C =2 \Rightarrow \frac{ x }{ y }+ y =2$
Put $x=-3$, we get
$-3+y^2=2 y \Rightarrow(y+1)(y-3)=0 $
$\text { As } y >0$
$\text { So, } y(x=-3)=3 . $