Question

The solution for the differential equation $\frac{ dy }{ y }+\frac{ dx }{ x }=0$ is

• A. $\frac{1}{y} + \frac{1}{x} = c $
• B. $\log \, x . \log \, y = c$
• C. $x \, y = c$
• D. $x + y = c$

Answer 1

Answer: (C)

We have, $\frac{d y}{y}+\frac{d x}{x}=0$
On integrating both sides, we get
$\log\, y+\log \,x=\log \,c$
$\Rightarrow \log \,x y=\log \,c$
$x y=c$