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

Pages: 1271 - 1278, Issue Special, September 2011

 Abstract        Full Text (258.8K)              

Adnan H. Sabuwala - Department of Mathematics, 5245 N. Backer Ave, M/S PB 108, Fresno, CA 93740-8001, United States (email)
Doreen De Leon - Department of Mathematics, 5245 N. Backer Ave, M/S PB 108, Fresno, CA 93740-8001, United States (email)

Abstract: The Euler-Cauchy differential equation is one of the first, and simplest, forms of a higher order non-constant coefficient ordinary di erential 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:  Euler-Cauchy, polynomial inhomogeneities, particular solution, non- homogeneous
Mathematics Subject Classification:  Primary: 34-01; Secondary: 34A05

Received: July 2010;      Revised: August 2010;      Published: October 2011.