Answer :

If y = f(x) is solution of a differential equation, then differentiating y = f(x) will give the same differential equation

Let us find the differential equation by differentiating y with respect to x

⇒ tan^{-1}x + tan^{-1}y = c

Differentiating with respect to x

⇒ (1 + y^{2})dx + (1 + x^{2})dy = 0

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