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Classroom note: Superposition: new solutions from known solutions

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Abstract:

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the contributions of several well-known mathematicians and also highlights their relationships to and interactions with one another, to lay the ground work for superposition theorems for solutions to linear differential equations that will be proven a short time later; and to illustrate one of the major differences between the type of results one can obtain for linear differential equations versus nonlinear differential equations.

Document Type: Research Article

DOI: https://doi.org/10.1080/0020739031000148958

Affiliations: Department of Mathematics and Computer Science Indiana State University Terre Haute IN 47809 USA, Email: macrobe@isugw.indstate.edu

Publication date: 2003-07-01

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