<abstract xmlns="http://www.w3.org/1999/xhtml"> For n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, with the general solution of n-th homogeneous linear differential equation with constant coefficients attached, to write the general solution of n-th linear differential equation with the given constant coefficients. In all the works that deal with this issue three situations are analyzed: the situation in which the free term is a polynomial P(x), the situation in which the free term is like P(x)· eα·x and lastly, the situation in which the free term is like eω·x · (P(x)· cos(β·x)+ Q(x)·sin(β·x)). In this study we aim to analyze if the free term is a combination of the three cases mentioned.</abstract>

For n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, with the general solution of n-th homogeneous linear differential equation with constant coefficients attached, to write the general solution of n-th linear differential equation with the given constant coefficients. In all the works that deal with this issue three situations are analyzed: the situation in which the free term is a polynomial P(x), the situation in which the free term is like P(x)· eα·x and lastly, the situation in which the free term is like eω·x · (P(x)· cos(β·x)+ Q(x)·sin(β·x)). In this study we aim to analyze if the free term is a combination of the three cases mentioned.

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients

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This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

For n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then,...

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients

Published Online: Jul 22, 2017

Page range: 24 - 29

DOI: https://doi.org/10.1515/kbo-2017-0151

Keywords
n-th order linear differential equations with constant coefficients, n-th order homogeneous linear differential equations with constant coefficients, particular solution, general solution

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients

Published Online: Jul 22, 2017

Page range: 24 - 29

DOI: https://doi.org/10.1515/kbo-2017-0151

Keywordsn-th order linear differential equations with constant coefficients, n-th order homogeneous linear differential equations with constant coefficients, particular solution, general solution

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
n-th order linear differential equations with constant coefficients, n-th order homogeneous linear differential equations with constant coefficients, particular solution, general solution