The solution of differential equation xdy - ydx = 0 represents

The correct answer is Option (3) → straight line passing through origin ##

Given that, $xdy - ydx = 0$

$⇒xdy = ydx$

$⇒\frac{dy}{y} = \frac{dx}{x} \quad \text{[applying variable separable method]}$

On integrating both sides, we get

$\log y = \log x + \log C$

$⇒ \log y = \log Cx ⇒ y = Cx$

which is a straight line passing through origin.