if y=x+1/y prove that (x^2-y^2+3)dy/dx=1 need the answer fast urgent.

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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