Solution of the differential equation $\frac{dx}{x}+\frac{dy}{y}=0$ is

The correct option is C $xy=c$

$\frac{dx}{x}+\frac{dy}{y}=0$

Integrating , we get

$\Rightarrow \int \frac{dx}{x}+\int \frac{dy}{y}=0$

$\Rightarrow \log \left(x\right)+\log \left(y\right)=k$

$\Rightarrow xy=e^k=c$

$\Rightarrow xy=c$

Hence, option C is correct.