Question

Solution of Differential Equating xdy – ydx = 0 represents

• A. A rectangular Hyperbola
• B. Parabola whose vertex is at origin
• C. Straight line passing through origin
• D. A circle whose centre is origin

Answer 1

The Correct Option is C

The given differential equation is: \[ xdy - ydx = 0 \] Rearranging terms: \[ \frac{dy}{dx} = \frac{y}{x} \] This is a separable differential equation. By separating variables: \[ \frac{dy}{y} = \frac{dx}{x} \] Integrating both sides: \[ \ln|y| = \ln|x| + C \] This implies: \[ y = Cx \]

So, the correct answer is (C) : Straight line passing through origin.