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Reduction of order as a neglected method for the solution of inhomogeneous linear ordinary differential equations. (English) Zbl 0697.34013

Summary: This paper shows that the method of ‘reduction of order’ is both a simpler way of teaching and of obtaining solutions for inhomogeneous linear ordinary differential equations than is the normally espoused method of ‘variation of parameters’. Details are given of the results of the method for the general nth order equation and the two methods are compared for \(n=2,3\). It will be noted that the proposed method takes a particularly simple form when the right-hand side of the equation is a multiple of one of the solutions to the related homogeneous equation.

MSC:

34A30 Linear ordinary differential equations and systems
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References:

[1] Bajpai A. C, Mathematics for Engineers and Scientists (1973) · Zbl 0301.00001
[2] Kreysig E., Advanced Engineering Mathematics (1983)
[3] O’Neil P. V., Advanced Engineering Mathematics (1987)
[4] Thomas G. B., Calculus and Analytic Geometry (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.