The solution of the differential equation xdy - ydx = 0 represent fam…

x dy - y dx = 0

so x dy = y dx

so $\int \frac{dy}{y} = \int \frac{dx}{x}$   (integrating both sides)

⇒ log y = log x + log C  →  taking logarithm constant for case of calculation 

⇒ log y = log Cx 

⇒ y = Cx  →  family of lines passing through O(0, 0)