`tan^(-1) x+tan^(-1)y=C` is general solution of the differential equation

Options

A. `(dy)/(dx)=(1+y^(2))/(1+x^(2))`
B. `(dy)/(dx)=(1+x^(2))/(1+y^(2))`
C. `(1+x^(2))dy+1(1+y^(2))dx=0`
D. `(1+x^(2))dx+1(1+y^(2))dy=0`

Explanation

To find the differential equation for which \( \tan^{-1} x + \tan^{-1} y = C \) is the general solution, we can follow these steps:

### Step 1: Differentiate both sides
We start by differentiating both sides of the equation with respect to \( x \).

\[ \frac{d}{dx}(\tan^{-1} x + \tan^{-1} y) = \frac{d}{dx}(C) \]
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