Using an exact third-order NL di®erential equation for the molecular state probability, we develop a variational approach which enables us to construct highly accurate analytic approximations describing time dynamics of the coupled atom-molecular system in each of the interaction regimes. We show that the approximation describing time evolution of the molecular state probability both in the weak interaction limit and in the large detuning regime of the strong interaction limit can be written as a sum of two distinct terms; the ¯rst one, being a solution to a limit ¯rst-order NL equation, e®ectively describes the process of the molecule formation while the second one, being a scaled solution to the linear DK problemb (but now with modi¯ed parameters), models the remaining oscillations which come up when the process of molecule formation is over. The graphs of the approximate and numerical solutions are practically indistinguishable for almost all the time range.