Integrating Factor Method: Applications & Construction in Solving Ordinary Differential Equations

The Integrating factor method is a crucial technique for solving ordinary differential equations. This paper aims to introduce various integral factors and their constructions, and apply them to special first-order ordinary differential equations, as well as high order ones. We examine the differences between construction methods of integral factors and verify the existence of integral factors for some specific types of first-order ordinary differential equations. Furthermore, we strive to gain a deeper understanding of how integral factors can be effectively applied to higher-order ordinary differential equations.