Another Approach to a Standard Differential Equation

Another Approach to a Standard Differential Equation

Author (s): R.S. Luthar

The Two-Year College Mathematics Journal. Vol. 10, No. 3 (Jun., 1979), pp. 200-201.

Published by: Mathematical Association of America

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Tags: Higher-order equations and linear systems

Abstract. This paper outlines a method by which when solving non-homogeneous second order linear differential equations one does not have to solve separately for the homogeneous and particular solution. The equations that Dr. Luthar is referring to are of the form, $y'' + Ay' + By = f(x)$. This is somewhat limiting in that the coefficient on the second order term must be zero. The author also states that this method could be generalized to higher order differential equations. After introducing the type of equation the author then outlines the method by which he solves the equation. Using a substitution to make the equation look like a first order linear equation he then solves it by that method. This method is very specific in the types of problems that it targets, is seemingly more difficult than the method of undetermined coefficients, and if anything conceals the significance of a homogeneous or particular solution. Austin E. Townsend, Stephen F. Austin State University, May 3, 2017.

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