This chapter will offer a large number of examples of ordinary differential equations and solution techniques so that the breadth of the application of these techniques may be illustrated. Aside from being one of the pillars of mathematical modeling, these equations are useful for almost everything around us [1–8] We will also explore their applications in various fields, from modeling disease spread in epidemiology to studying the chaotic systems of chaos theory. By exploring these varied applications, we will illustrate how ordinary differential equations serve as a foundation for studying complex systems and provide insights into a wide array of phenomena, ranging from population dynamics and ecological modeling to the behavior of physical systems and the prediction of chaotic behavior. It acts as both an entry point into the material and a comprehensive overview of the practical implications of these mathematical models, with real-world applications for scientific and engineering challenges that make up the bulk of the remaining chapters.