The general solution of differential equation $x d y-y d x=0$ represents
The general solution of differential equation $x d y-y d x=0$ represents
the circle whose centre is at the origin
a straight line passing through the origin
a rectangular hyperbola
the parabola whose vertex is at the origin.
Solution
$\begin{aligned} & x d y-y d x=0 \Rightarrow \int \frac{d y}{y}=\int \frac{d x}{x} \\ & \Rightarrow \log y=\log x+\log c \\ & \Rightarrow \log y=\log c x \\ & \Rightarrow y=c x\end{aligned}$
which is a straight line passing through the origin