`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

Given, that `tan^(-1)y=C`
On differentiating w.r.t. we get
`(1)/(1+x^(2))+(1)/(1+y^(2)).(dy)/(dx)=0`
`Rightarrow (1)/(1+y^(2)).(dy)/(dx)=(1)/(1+x^(2))`
`Rightarrow (1+x^(2))+(1+y^(2))dx=0`