Solution of differential equation xdy ? ydx = 0 represents:

Question

Solution of differential equation $x d y - y d x = 0$ represents:

Smart Achievers · Accepted Answer

(1)

Ans. family of straight lines passing through origin

Explanation:

Given, $x d y - y d x = 0$

$x d y = y d x$

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

On integrating both sides, we get

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

$\log y = \log c x$

$\Rightarrow$ $y = c x$

A straight line passes through origin.

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