Unification of the common methods for solving the first-order linear ordinary differential equations

A good understanding of the mathematical processes solving first-order linear ordinary differential equations (ODEs) is foundation for undergraduate students in science and engineering programs to progress smoothly advanced ODEs and/or partial (PDEs) later. However, different methods are presented various textbooks resources, which often confuses their choice method ODEs. This special tutorial note presents practices author used address such confusions engaged bachelorette studies at a regional university Australia recent years. The derivation four commonly adopted ODEs, including three explicit one implicit many textbooks, first, followed by logical interconnections that unify these clarify student's on presentations procedures solutions sources. Comparisons among also made.