Systems of Inhomogenous Differential Equations, the Use of EXCEL, and an Application

Abstract

The solution to systems of differential equations is almost immediate by using one of the numerous available commercial computer programs. The purpose of this paper is to present an elementary analytical method for solving systems of linear first-order ordinary differential equations with constant coefficients in the presence of inhomogeneous terms, that will be suitable to create phase diagrams by EXCEL. A phase diagram of a dynamic system contains the steady-state, one path depending on an initial point, and — if available — stable or unstable arms (linear paths, which go through the steady-state). Additionally, arrows represent the directions of motion for four different regions. Furthermore, we affect the fineness of plotting points by variation of a scale, i.e. the graph can show a continuous path or the speed of motion.