Solve the differential equation: 2√(xy)(dy)/(dx) = 1, where x and y are both greater than 0.

Which of the following options correctly represents the solution to this equation?

A) 2√(xy) = x + C, where C is a constant
B) (2/3)√(xy) = x + C, where C is a constant
C) (1/2)√(xy) = x + C, where C is a constant
D) √(xy) = x + C, where C is a constant