This Books deals with the census survey report on a City and observe that the population of a City were increasing in an exponential manner. In order to project the population of a City for the next several decades the Malthusian exponential model was considered. The model is a first order ordinary differential equation (O.D.E) parametrized by the growth rate of the population. In order to include the immigrant population, Necessary modifications of the model were made, which is again an exponential model where the growth rate is the sum of the actual growth rate and immigrant rate .The existing classical solution of the differential equation model as an initial value problem (I.V.P) for both the time independent and time dependent growth rate i.e., for both autonomous and non-autonomous cases.Error estimation of the numerical solution was performed to justify the correctness of the implementation by using computer programming. Finally, the predicted populations for the both autonomous and non-autonomous cases are presented.