The solution of the differential equation $x \dfrac{d y}{d x}=\cot y$ is

The given differential equation is $x \dfrac{dy}{dx} = \cot y$.

Separating the variables, we get $\dfrac{dy}{\cot y} = \dfrac{dx}{x}$.

This simplifies to $\tan y \, dy = \dfrac{dx}{x}$.

Integrating both sides, we have $\int \tan y \, dy = \int \dfrac{dx}{x}$.

The integral of $\tan y$ is $\ln |\sec y|$ or $-\ln |\cos y|$.

Thus, $-\ln |\cos y| = \ln |x| + C$.

Rearranging the terms, $\ln |x| + \ln |\cos y| = -C$.

Using the property of logarithms, $\ln |x \cos y| = C'$, where $C' = -C$.

Taking the exponential of both sides, $x \cos y = e^{C'} = c$.

Answer: $x \cos y=c$