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. $xy=c$
• D. $x+y=c$

Answer 1

The correct option is C $xy=c$

$\frac{dy}{y}+\frac{dx}{x}=0$
$\Rightarrow \frac{dy}{y}=-\frac{dx}{x}$
Integrating both sides, we get
$\log y=-\log x+\log c,$ where $c$ is a constant.
$\Rightarrow \log xy=\log c$
$\Rightarrow xy=c$