Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities

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2011, 2011(Special): 1271-1278. doi: 10.3934/proc.2011.2011.1271

Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities

Adnan H. Sabuwala ^1, and Doreen De Leon ^1,

1.	Department of Mathematics, 5245 N. Backer Ave, M/S PB 108, Fresno, CA 93740-8001, United States, United States

Received July 2010 Revised August 2010 Published October 2011

Abstract
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The Euler-Cauchy differential equation is one of the first, and simplest, forms of a higher order non-constant coefficient ordinary dierential equation that is encountered in an undergraduate differential equations course. For a non-homogeneous Euler-Cauchy equation, the particular solution is typically determined by either using the method of variation of parameters or transforming the equation to a constant-coefficient equation and applying the method of undetermined coefficients. This paper demonstrates the surprising form of the particular solution for the most general n$^(th)$ order Euler-Cauchy equation when the non-homogeneity is a polynomial. In addition, a formula that can be used to compute the unknown coecients in the form of the particular solution is presented.

Keywords: polynomial inhomogeneities, non- homogeneous, particular solution, Euler-Cauchy.

Mathematics Subject Classification: Primary: 34-01; Secondary: 34A05.

Citation: Adnan H. Sabuwala, Doreen De Leon. Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities. Conference Publications, 2011, 2011 (Special) : 1271-1278. doi: 10.3934/proc.2011.2011.1271

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