In the numerical simulations of ship maneuvering, a set of ordinary differential equations with constant coefficients is traditionally used. However, when the transient external forces due to rudder motions and waves are concerned, this type of equations of motions is not precise in a strict sense. But the research on the relationship between two types equations is sparse. Therefore, in this paper, the study has been made to clear the relations between them. For this purpose, based on the Strip Theory which is practicaly used to evaluate the seakeeping quality of a ship, the equation of motion described in the time domain with a convolution integral is derived. And by the analytical and numerical considerations, the comparisons of two types equations of motions have been made.