<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In this contribution we compare solutions of second order linear differential equations with constant coefficients with respect to the form of right-hand side of the equation and to the form of initial or boundary conditions. We will see that some types of such differential equations one can resolve by the method of variation of constants and it is not possible solve them by Laplace transform. On the other hand, some of them are solvable by Laplace transform and are unsolvable by the method of variation of constants. The reason for the comparison is to show that the students of automation have to know both ways of solving linear differential equations with constant coefficients.</p></abstract>

In this contribution we compare solutions of second order linear differential equations with constant coefficients with respect to the form of right-hand side of the equation and to the form of initial or boundary conditions. We will see that some types of such differential equations one can resolve by the method of variation of constants and it is not possible solve them by Laplace transform. On the other hand, some of them are solvable by Laplace transform and are unsolvable by the method of variation of constants. The reason for the comparison is to show that the students of automation have to know both ways of solving linear differential equations with constant coefficients.

Comparsion of Solutions of Second Order Linear Differential Equations With Constant Coefficients

Department of Mathematics, Institute of Applied Informatics, Automation and Mathematics, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology Bratislava, Hajdóczyho 1, 917 24 Trnava

Research Papers Faculty of Materials Science and Technology Slovak University of Technology

In this contribution we compare solutions of second order linear differential equations with constant coefficients with respect to the form of right-hand side...

Comparsion of Solutions of Second Order Linear Differential Equations With Constant Coefficients

Published Online: Mar 03, 2011

Page range: 151 - 155

DOI: https://doi.org/10.2478/v10186-010-0018-y

Keywords
linear differential equation, Laplace transform, variation of constants

This content is open access.

Comparsion of Solutions of Second Order Linear Differential Equations With Constant Coefficients

Published Online: Mar 03, 2011

Page range: 151 - 155

DOI: https://doi.org/10.2478/v10186-010-0018-y

Keywordslinear differential equation, Laplace transform, variation of constants

This content is open access.

Keywords
linear differential equation, Laplace transform, variation of constants