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  4. The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

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Q. The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

VITEEEVITEEE 2014Differential Equations

Solution:

The differential equation of the rectangular hyperbola $xy = c^2$ is
$ y + x \frac{dy}{dx} = 0 $
$\Rightarrow x \frac{dy}{dx} = - y $