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  4. The solution of the differential equation xdy + ydx = 0 is:

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Q. The solution of the differential equation xdy + ydx = 0 is:

Differential Equations

Solution:

Given, xdy + ydx = 0
Divide both sides above equation by xy,
We get, $\frac{dx}{dy} + \frac{dy}{y} = 0 $
Integrating it on both sides, we get
log x + log y = log c
$\Rightarrow $ log xy = log c $\Rightarrow $ xy = c.