Mathematical Problems in Engineering 
Volume 2008 (2008), Article ID 654820, 7 pages
doi:10.1155/2008/654820
Research Article

Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System

M. Legua,1 I. Morales,2 and L. M. Sánchez Ruiz3

 1Departamento de Matemática Aplicada, Centro Politécnico Superior (CPS), Universidad de Zaragoza, 50015 Zaragoza, Spain
2Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Agrónomos (ETSIA), and (IUMPA), Universidad Politécnica de Valencia, 46022 Valencia, Spain
3Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería del Diseño (ETSID), and Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, 46022 Valencia, Spain
Received 16 June 2008; Accepted 26 July 2008

Recommended by Carlo Cattani

Abstract

In signal processing, a pulse means a rapid change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. A square wave function may be viewed as a pulse that repeats its occurrence periodically but the return to the baseline value takes some time to happen. When these periodic functions act as inputs in dynamic systems, the standard tool commonly used to solve the associated initial value problem (IVP) is Laplace transform and its inverse. We show how a computer algebra system may also provide the solution of these IVP straight forwardly by adequately introducing the periodic input.