Question

The solution of the differential equation $xdy — ydx = 0$ represent family of

• A. Circles passing through origin.
• B. Straight line parsing through (-1. 6)
• C. Straight line passing through the origin.
• D. Circle whose center is at the origin.

Answer 1

Answer: (C)

Straight line passing through the origin.

Answer 2

The differential equation that is provide : $xdy – ydx = 0$

$\Rightarrow\frac{dy}{dx}=\frac{x}{y}$

$\Rightarrow \frac{dy}{y}=\frac{dx}{x}$

performing integration on two sides, we find

$\int\frac{dy}{y}=\frac{dx}{x}$

$\Rightarrow \log\;y= \log \; x+ \log c$

$\Rightarrow \log y=\log xc$

$\Rightarrow y = xc$

That indicated that it is straight line passing through the origin.

Hence, the correct option is (C):Straight line passing through the origin.