Comparative analysis of first-order linear differential equations and arithmetic methods in projecting Surakarta City's population - Yoga Tegar Santosa; Dini Wardani Maulida; Berliani Ardelia Sukowati; Mutiara Hisda Mahmudah (Journal Focus Action of Research Mathematic (Factor M), 2025)
Population estimates are needed to project future populations, allowing for preparation in facing the possible impacts of population growth. This study aims to find a general formula or formula for the first-order linear differential equation and the arithmetic method based on the average value of the error of both, in projecting the population in Surakarta City in the future, and to determine the method that has a higher level of accuracy. This study is included in the category of descriptive research with a quantitative approach. Data were collected through literature studies and documentation of the population in Surakarta City from 2016 to 2024. Meanwhile, data analysis was carried out using quantitative descriptive analysis and comparative analysis. The study results show that the formula obtained for the first-order linear differential equation method is N(t)=562801 exp(0.0071997706t. While the formula obtained for the arithmetic method is Pt = 562801 (1+0.007357544t). From the comparison of the two methods, the arithmetic method is proven to be more accurate because it has a smaller average error (MAPE-based) than the first-order linear differential equation method.  These results can provide insight into the best methods for estimating population growth as the basis for population policy planning and regional development.