Alternative solution of the inhomogeneous linear differential equation of order two

In this paper, we present an alternative method for solving the general inhomogeneous linear ordinary differential equation (ODE) of order two. The solution appears in the standard form as the sum of the solution of the equivalent homogeneous problem and the particular solution of the inhomogeneous...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 339; no. 1; pp. 582 - 589
Main Authors Johnson, P., Busawon, K., Barbot, J.P.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.03.2008
Elsevier
Subjects
Exact sciences and technology
Exact solutions
Inhomogeneous equations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Ordinary differential equations
Inhomogeneous equations
Exact solutions
Linear equation
Mathematical analysis
Differential equation
Particular solution
Klein Gordon equation
Exact solution
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Summary:In this paper, we present an alternative method for solving the general inhomogeneous linear ordinary differential equation (ODE) of order two. The solution appears in the standard form as the sum of the solution of the equivalent homogeneous problem and the particular solution of the inhomogeneous problem at hand. The main advantage of the method exposed herein is that the particular solution is computable from two different integrals. This allows the problem solver to choose the simplest integral with which to work with in order to get the final solution. For illustrative purposes we employ the method presented to aid in the solution of some example problems including the inhomogeneous Klein–Gordon equation.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.06.056