ify=x+1/y prove that (x^2-y^2+3)dy/dx=1

Dear Aritra,

Solution:-  y = x +1/y.................(1)

              dy/dx = 1 - (1/y2) (dy/dx)

           [1 + (1/y2)] (dy/dx) = 1..................(2)

        From eq. (1), y-1/y = x. On squaring both sides, we get-

 (y-1/y )2= x2 or  y2 + 1/y2 -2= x2 or 1/y2 = (x2 - y2+2)

Putting the value of 1/y2  in eq. (2), we get-

  [1 + (x2 - y2+2)] (dy/dx) = 1

(x2 - y2+3) (dy/dx) = 1

Hence proved.                       

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