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The solution of the differential equation $xdy-ydx = 0$ represents |
straight line passing through origin a circle whose centre is at origin a rectangular hyperbola parabola whose vertex is at origin |
straight line passing through origin |
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 |
