The solution of the differential equation xdy ? ydx = 0 represent family of:

Question

The solution of the differential equation $x d y - y d x = 0$ represent family of:

Smart Achievers · Accepted Answer

(3)

Ans. Straight line passing through the origin

Explanation:

$x d y - y d x = 0$

$\frac{1}{y} d y = \frac{1}{x} d x$

On integrating both side,

$\int \frac{1}{y} d y = \int \frac{1}{x} d x$

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

$\log y = \log (c x)$

$y = c x$

It is equation of straight line passing through origin.

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