Q. 483.7( 3 Votes )

# tan^{-1}x + tan^{-1} y = c is the general solution of the differential equation:

A.

B.

C. (1 + x^{2}) dy + (1 + y^{2}) dx = 0

D. (1 + x^{2}) dx + (1 + y^{2}) dy = 0

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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