<abstract xmlns="http://www.w3.org/1999/xhtml">

A particular solution for the n-th order linear differential equations with constant coefficients that are free of term such as <italic>P</italic>(<italic>x</italic>)· <italic>e</italic><italic>a</italic>·<italic>x</italic> ·cos<italic>n</italic><italic>x</italic> or/and <italic>Q</italic>(<italic>x</italic>)·<italic>e</italic><italic>b</italic>·<italic>x</italic>· sin<italic>n</italic><italic>x</italic>, <italic>n</italic>∈ <italic>N</italic>, can be determined based on two elements: the way in which cos<italic>n</italic><italic>x</italic> and sin<italic>n</italic><italic>x</italic> can develop, and, on the other hand on the way a particular solution for the free terms <italic>P</italic>(<italic>x</italic>) ·<italic>e</italic><italic>a</italic>·<italic>x</italic>·cos<italic>n</italic><italic>x</italic> or/and <italic>Q</italic>(<italic>x</italic>)·<italic>e</italic><italic>b</italic>·<italic>x</italic>·sin<italic>m</italic><italic>x</italic>, <italic>n</italic> ∈<italic>N</italic> is sought. We can, of course, write the way a particular solution looks also in the case we have a combination of the two terms or more terms of this kind.
</abstract>

A particular solution for the n-th order linear differential equations with constant coefficients that are free of term such as P(x)· ea·x ·cosnx or/and Q(x)·eb·x· sinnx, n∈ N, can be determined based on two elements: the way in which cosnx and sinnx can develop, and, on the other hand on the way a particular solution for the free terms P(x) ·ea·x·cosnx or/and Q(x)·eb·x·sinmx, n ∈N is sought. We can, of course, write the way a particular solution looks also in the case we have a combination of the two terms or more terms of this kind.

Determining a Particular Solution for <italic>N</italic>-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form <italic>e</italic><italic>a</italic>·<italic>x</italic>·<italic>P</italic>(<italic>x</italic>) ·cos<italic>n</italic><italic>x</italic> or <italic>e</italic><italic>b</italic>·<italic>x</italic>·<italic>Q</italic>(<italic>x</italic>)·sin<italic>n</italic><italic>x</italic>

International conference KNOWLEDGE-BASED ORGANIZATION

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Determining a Particular Solution for -th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form ·() ·cos or ·()·sin

A particular solution for the n-th order linear differential equations with constant coefficients that are free of term such as P(x)· ea·x ·cosnx or/and...

Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form e^a^·^x·P(x) ·cosⁿx or e^b^·^x·Q(x)·sinⁿx

Published Online: Jul 20, 2020

Page range: 49 - 54

DOI: https://doi.org/10.2478/kbo-2020-0114

Keywords
th order linear differential equations with constant coefficients, particular solution, general solution, free term of the following form () ·· cos or/and ()·· sin

© 2020 Vasile Căruţaşu et al., published by Sciendo

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

Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

Published Online: Jul 20, 2020

Page range: 49 - 54

DOI: https://doi.org/10.2478/kbo-2020-0114

Keywordsth order linear differential equations with constant coefficients, particular solution, general solution, free term of the following form () ·· cos or/and ()·· sin

© 2020 Vasile Căruţaşu et al., published by Sciendo

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

Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form e^a^·^x·P(x) ·cosⁿx or e^b^·^x·Q(x)·sinⁿx

Keywords
th order linear differential equations with constant coefficients, particular solution, general solution, free term of the following form () ·· cos or/and ()·· sin