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

The determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms functions such as <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>, or/and <italic>e</italic><italic>b</italic>·<italic>x</italic>·<italic>Q</italic>(<italic>x</italic>) sin<italic>n</italic><italic>x</italic>, <italic>n</italic> ∈ <italic>N</italic>, is based on the expansion of cos<italic>n x</italic> and sin<italic>n x</italic>, and, on the other hand, on how a particular solution for a column of free terms with functions such as <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, n</italic> ∈ <italic>N</italic>, looks like. We can also write the way a particular solution looks like when we have a combination of two or more functions on the 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>, <italic>n</italic> ∈ <italic>N</italic> in the column of free terms.
</abstract>

The determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, or/and eb·x·Q(x) sinnx, n ∈ N, is based on the expansion of cosn x and sinn x, and, on the other hand, on how a particular solution for a column of free terms with functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N, looks like. We can also write the way a particular solution looks like when we have a combination of two or more functions on the form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N in the column of free terms.

Determining a Particular Solution for Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As <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 Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As ·() ·cos or ·()·sin

The determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms...

Determining a Particular Solution for Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As e^a^·^x·P(x) ·cosⁿx or e^b^·^x·Q(x)·sinⁿx

Pubblicato online: 20 lug 2020

Pagine: 55 - 64

DOI: https://doi.org/10.2478/kbo-2020-0115

Parole chiave
systems of linear differential equations with constant coefficients, particular solution, general solution, column of free terms with functions such as () · ·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 Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

Pubblicato online: 20 lug 2020

Pagine: 55 - 64

DOI: https://doi.org/10.2478/kbo-2020-0115

Parole chiavesystems of linear differential equations with constant coefficients, particular solution, general solution, column of free terms with functions such as () · ·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 Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As e^a^·^x·P(x) ·cosⁿx or e^b^·^x·Q(x)·sinⁿx

Parole chiave
systems of linear differential equations with constant coefficients, particular solution, general solution, column of free terms with functions such as () · ·cos or/and () ·· sin