Mathematics in Motion: Linear Systems of Differential Equations on the Differential Analyzer

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of autonomous dierential equations and the traditional analytical method for finding a solution, I will run some of these systems on the dierential analyzer. With this visual approach, we look at the behavior of the rates of change to study the equilibrium solutions. I want to give a mechanical description of the relationship between the equations of the system