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)

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.