The solution of the differential equation xdy-ydx = 0 represents

The correct answer is Option (1) → straight line passing through origin

Given differential equation: $x \, dy - y \, dx = 0 \Rightarrow \frac{dy}{dx} = \frac{y}{x}$

Separate variables: $\frac{dy}{y} = \frac{dx}{x}$

Integrate: $\ln|y| = \ln|x| + C \Rightarrow \ln|y| - \ln|x| = C \Rightarrow \ln\left|\frac{y}{x}\right| = C$

$\Rightarrow \frac{y}{x} = k \Rightarrow y = kx$

Thus, solution represents straight lines passing through the origin.

Answer: straight line passing through origin