Question

Solution of differential equation xdy – ydx = 0 represents : ______.

Options

• A rectangular hyperbola

• Parabola whose vertex is at origin

• Straight line passing through origin

• A circle whose centre is at origin

Answer 1

Solution of differential equation xdy – ydx = 0 represents : straight line passing through origin.

Explanation:

The given differential equation is xdy – ydx = 0

⇒ `("d"y)/("d"x) = y/x`

⇒ `("d"y)/y = ("d"x)/x`

Integrating both sides, we get

`int ("d"y)/y = ("d"x)/x`

⇒ log y = log x + log c

⇒ log y = log xc

⇒ y = xc

Which is a straight line passing through the origin.