Solution of differential equation xdy – ydx = 0 represents

a rectangular hyperbola straight line passing through origin parabola whose vertex is at origin circle whose centre is at origin

straight line passing through origin

$x d y-y dx=0 \Rightarrow \frac{d y}{y}-\frac{d x}{x}=0 $ ⇒ log y log x = log c $\Rightarrow \log \left(\frac{y}{x}\right)=\log c$ $\Rightarrow \frac{y}{x}=c$ or y = cx which is a straight line. Hence (2) is the correct answer.