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Abstract

First order linear nonautonomous homogenous systems of differential equations are characterized by a matrix differential equation where the matrix is a function of the independent variable. These nonautonomous systems are used extensively in the study of Floquet and Lyapunov theories, and the applications of such systems reaches into fields such as physics, biology, and engineering. The following paper develops a technique for finding the closed form solution to a 2×2 nonautonomous system. The paper shows that the solution to such a system is directly related to the solution of a Riccati differential equation constructed from the coefficients of the system's matrix. The primary findings also demonstrate that the system can be solved exactly if a solution to the corresponding Riccati equation can be determined.

Author Bio

Alexander Shveyd is physics major and a senior at the University of California, Riverside. As a burgeoning physicist he enjoys investigating topics in applied mathematics because he believes advances in this field could result in theoretical developments for the physical sciences. The subject of differential equations is of particular interest to him. The research for the following paper came about while working on a classical mechanics problem dealing with moments of inertia using techniques he studied in a class on ordinary differential equations. After graduation in 2005, Alexander plans to continue on to graduate school where he hopes to conduct both theoretical and experimental research in the field of solid state physics.

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