The solution of differential equation x dy - y dx = 0 represents:

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. straight line passing through origin

Explanation:

Given that,

$x d y - y d x = 0$

$\Rightarrow$ $x d y = y d x$

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

On integrating both sides, we get

$\log y = \log x + \log C$

$\Rightarrow$ $\log y = \log C x$

$\Rightarrow$ $y = C x$

which is a straight line passing through origin.

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