Question

Solution of differential equation xdy - ydx = 0 represents:

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

Answer 1

Answer: (D)

straight line passing through origin.

Answer 2

Given: xdy - ydx = 0 Dividing by xy on both sides, we get: $\frac{dy}{y} - \frac{dx}{x} = 0$ $\Rightarrow \, \frac{dy}{y} = \frac{dx}{x}$ By integrating on both sides, we get, log y = log x + log c $\Rightarrow \, \log \frac{y}{x} = \log c$ $\Rightarrow \, y = cx$ or $y - cx = 0$ which represents a straight line passing through origin.