This article examines several applications of ordinary differential equations (ODEs) in specific industries and in everyday life. This project encourages the integration of ODEs into the undergraduate curriculum through the use of real-world analogies, primarily examining the dynamics of international transactions, although ODEs are often applied in areas such as population dynamics, electronics, and the physics of Featuring an arms race at the center and similar to predator-prey dynamics Richardson was a pioneer in the development of mathematical models for understanding wars and arms races between nations. The importance of imbalances in weapon strategies is emphasized in the study, which discusses the evolution of ODEs representing continuous progress between bilateral states or alliances in terms of their sufficiency. It also emphasizes the ability to represent complexity in a variety of educational contexts and promotes a best-practice understanding of how to use mathematics effectively. The analysis is a novel model for predicting decay behaviour and population growth using differential equations. It teaches how to use well-known basic rules and concepts to develop ODE-based models and demonstrates versatility in many situations. This study highlights the critical role of ODEs in representing and predicting dynamic interactions, highlighting their importance in understanding, analyzing and possibly reducing social interactions and complex real-world conflicts. It emphasizes the bottom line.