1) The solution of the differential equation $\left\{1+x\sqrt{(x^{2}+y^{2})}\right\}dx + \left\{\sqrt{(x^{2}+y^{2})}-1\right\}ydy = 0 is ? A) x2+y22+13(x2+y2)3/2=C B) x−y23+12(x2+y2)1/2=C C) x−y22+13(x2+y2)3/2=C D) None of these Answer: Option CExplanation:Rearranging the equation, we have dx - ydy + √(x2+y2)(xdx+ydy)=0 dx−ydy+12√(x2+y2)d(x2+y2)=0 On integrating, we get x−y22+12∫√tdt=C {t=√x2+y2} or x−y22+13(x2+y2)3/2=C