Question

Solution of differential equation $xdy-ydx = 0$ represents

• A. a rectangular hyperbola
• B. parabola whose vertex is at origin
• C. straight line passing through origin
• D. a circle whose centre is at origin

Answer 1

Answer: (C)

straight line passing through origin

Answer 2

$xdy-ydx=0$ $\Rightarrow \frac{dy}{y}=\frac{dx}{x}$ On integration, we get $logy = logx + logc$ $\Rightarrow y = xc$ which is equation of a straight line passing through origin.