Answer :

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


Re - writing the equation as



Now assuming 1+y2 = t2


Differentiating both sides, we get


ydy = tdt


Similarly, for LHS assuming 1+x2 = v2


differentiating both sides


xdx = vdv


substituting these values in the differential equation



Integrating both sides



Re - writing as



Using identity:



and



Integrating both sides, we get



Substituting the value of v and t in the above equation



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