This paper examines the effect of net migration on prospective population growth in Dhaka City for the next several years. The paper deals with the urban challenges in Bangladesh focusing on rapid urban growth in the megacity of Dhaka. Here Population of Dhaka city has been predicted with the help of an ordinary differential equation model known as Malthusian Exponential population model which is parameterized by growth rate. In order to include the immigrant population, we make necessary modification of the model, which is again an exponential model where the growth rate ( ) is the sum of the actual growth rate ( ) and immigrant rate ( ).We use fourth order Runge-Kutta scheme for the numerical solution of the autonomous and non-autonomous case where we incorporate the growth rate as a function of time. We perform error estimation of the numerical solution which justifies the correctness of the implementation by using computer programming. The procedure used in this study is by comparing two projected population scenarios one with constant growth rate and the other is time dependent growth rate based on the latest data collected through surveys of population censuses and relevant studies.