Re - writing the equation as

Now separating variable x on one side and variable y on another side, we have

Multiplying and dividing the numerator of LHS by x

Assuming 1+y² = t² and 1+x² = v²

Differentiating we get,

ydy = tdt

xdx = vdv

substituting these values in above differential equation

Integrating both sides

Adding 1 and subtracting 1 to the numerator of RHS

Using identities:

and

Substituting t and v in above equation