The general solution of the differential equaiton `(1+y^(2))dx+(1+x^(2))dy=0`, is

Options

A. `x-y = C (1-xy)`
B. `x-y = C(1+xy)`
C. `x+y=C (1-xy)`
D. `x+y = C (1+xy)`

Answer

c

Explanation

Given ` (dx)/(1+x^(2))+(dy)/(1+y^(2))=0`
` rArr tan^(-1) x + tan^(-1) y = tan^(-1) C ` [ integrating ]
` rArr (x+y)/(1-xy) = C rArr x + y = C (1-xy)`