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)

$x \, y = c$

Answer 2

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