Open AccessThe Characteristic Equation of the Euler-Cauchy Differential Equation and its Related Solution Using MATLAB
Author(s) -
Sundaraelangovan Selvam
Publication year - 2021
Publication title -
asian journal of science and applied technology
Language(s) - English
Resource type - Journals
ISSN - 2249-0698
DOI - 10.51983/ajsat-2021.10.1.2792
Subject(s) - homogeneous differential equation , mathematics , differential equation , euler method , integrating factor , bernoulli differential equation , exact differential equation , mathematical analysis , cauchy distribution , examples of differential equations , ordinary differential equation , euler's formula , initial value problem , cauchy problem , hyperbolic partial differential equation , linear differential equation , universal differential equation , euler equations , differential algebraic equation
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.