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

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

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x \frac{d y}{d x} = - y

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

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x d y + y d x = c

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Solution

The correct option is B $x \frac{d y}{d x} = - y$
The equation of hyperbola which has its asymptotes as the coordinate axes is given by $x y = c^{2}$ .
The differential equation of the rectangular hyperbola $x y = c^{2}$ is
$\frac{d}{d x} (x y) = \frac{d}{d x} c^{2}$
$⟹ y + x \frac{d y}{d x} = 0$
$⟹ x \frac{d y}{d x} = - y$
Hence, option B is correct.

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