The Characteristic Equation of the Euler-Cauchy Differential Equation and its Related Solution Using MATLAB
Keywords:Euler-Cauchy, Differential Equation, Ordinary Differential Equation, Characteristics Equation, MATLAB
The behavior of nature is usually modelled with Differential Equations in various forms. Depending on the constrains and the accuracy of a model, the connected equations may be more or less complicated. For simple models we may use Non Homogeneous Equations but in general, we have to deal with Homogeneous ones since from a physicists point of view nature seems to be Homogeneous. In many applications of sciences, for solving many of them, often appear equations of type nth order Linear differential equations, where the number of them is Euler-Cauchy differential equations. i.e. Euler-Cauchy differential equations often appear in analysis of computer algorithms, notably in analysis of quick sort and search trees; a number of physics and engineering applications. In this paper, the researcher aims to present the solutions of a homogeneous Euler-Cauchy differential equation from the roots of the characteristics equation related with this differential equation using MATLAB. It is hoped that this work can contribute to minimize the lag in teaching and learning of this important Ordinary Differential Equation.
S. H. Javadpour, “An Introduction to Ordinary and Partial Differential Equations,” Iran, Alavi, 1993.
F. B. Hilderbrand, “Advanced Calculus for Applications,” New Jersey, 1976.
S. T. Mohyud-Din, “Solutions of Nonlinear Differential Equations by Exp-function Method,” World Applied Sciences Journal, Vol. 7 (Special Issue for Applied Math), pp.116-147, 2009.
K. Batiha and B. Batiha, “A New Algorithm for solving Linear Ordinary Differential Equations,” World Applied Sciences Journal, Vol.15, No.12, pp.1774-1779, 2011.
Boyer and Carl, B. “Historian in Mathematics: Edgard Blucher,” 1974.
A. R. Forsyth, “Theory of differential equation,” Vol. 6, Cambridge University Press, 1906.
W. F. Ames, “Nonlinear partial differential equations in engineering,” Vol. 2, Academic Press, New York, 1972.
L. Qiusheng, C. Hong and L. Guiqing, Static and Dynamic of straight bars with variable cross-section, Computer & Structures, Vol. 59, No. 6, pp.1185-1191,1996.
L. Qiusheng, C. Hong and L. Guiqing, “Analysis of Free Vibrations of Tall Buildings,” Journal of Engineering Mechanics, Vol. 120, No. 9, pp.1861-1876, 1994.
Hua-Huai Chern and Hsien-Kuei Hwang, “Tsung-Hsi Tsai, An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms,” Journal of Algorithms, Vol. 44, pp. 177-225, 2002.
E. Kreyszig, "Advanced Engineering Mathematics", Wiley, ISBN 978-0470084847, 2006.
P. Dawkins, “Differential Equations,”Chapter-6, http://tutorial.math. lamar.edu/terms.aspx, 2007.