FFF #78. Solving a Second-order Differential Equation

FFF #78. Solving a Second-order Differential Equation

Author(s): Ed Barbeau

The College Mathematics Journal, Vol. 25, No. 5 (Nov., 1994), pp. 432-435.

Published by: Mathematical Association of America. Stable URL: https://www.jstor.org/stable/2687508

Tags: Higher-order equations and linear systems

Abstract. This paper originally appeared in a column titled Fallacies, Flaws, and Flimflam dedicated to examining fallacies that raise mathematical issues. In this particular case, the author introduces a method for finding a particular integral to a second-order differential equation that provides a solution to this equation. Although a solution is found, some assumptions are made that are not concretely proved. The primary method introduced for finding a solution consists of differentiating both sides of an intermediary equation until the right side vanishes, and at this point a term is set to zero. The primary issue here is that the argument is presented in prospect, but never proved. The conclusion is that while this method appears to work, it is not rigorously proved and relies on unsubstantiated assumptions. Samuel C. Jentsch, Stephen F. Austin State University, May 1, 2017.

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