Find the differential equation of the family of concentric circles $x^{2} + y^{2} = a^{2}$ .

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Solution

$x^{2} + y^{2} = a^{2}$
Differentiating w.r.t $x$ ,
$2 x + 2 y \frac{d y}{d x} = 0$ .
Now as $a$ is eliminated so this is the differential equation of the family of concentric circles.
$\Rightarrow \frac{d y}{d x} = - \frac{x}{y}$

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