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For n-th order linear differential equations with constant coefficients the problem of determining the general solution involves determining the general solution of the attached homogeneous equation and, on the other hand, determining a particular solution. This paper aims to analyze the conditions under which the general solution can be obtained for a n-th order linear differential equation with constant coefficients which have the free term in the following form P(x). ln xunder the condition that the attached characteristic equation hassingle real root of order of multiplicity n. For this we will use the method of variation of constants which leads us to a system whose solution we will gain using the Upper incomplete Gamma function.
</abstract>

For n-th order linear differential equations with constant coefficients the problem of determining the general solution involves determining the general solution of the attached homogeneous equation and, on the other hand, determining a particular solution. This paper aims to analyze the conditions under which the general solution can be obtained for a n-th order linear differential equation with constant coefficients which have the free term in the following form P(x). ln xunder the condition that the attached characteristic equation hassingle real root of order of multiplicity n. For this we will use the method of variation of constants which leads us to a system whose solution we will gain using the Upper incomplete Gamma function.

Determining a Particular Solution for <italic>n-th</italic> Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following form <italic>P</italic>(<italic>x</italic>). <italic>ln x</italic> and the Characteristic Equation Has a Real Root of Order of Multiplicity n

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Determining a Particular Solution for  Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following form ()  and the Characteristic Equation Has a Real Root of Order of Multiplicity n

For n-th order linear differential equations with constant coefficients the problem of determining the general solution involves determining the general...

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following form P(x)^. ln x and the Characteristic Equation Has a Real Root of Order of Multiplicity n

Pubblicato online: 06 lug 2022

Pagine: 32 - 38

DOI: https://doi.org/10.2478/kbo-2022-0084

Parole chiave
n-th order linear differential equations with constant coefficients, method of variation of constants, general solution, free term in the form () ln

© 2022 Vasile Căruţaşu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following form P(x). ln x and the Characteristic Equation Has a Real Root of Order of Multiplicity n

Pubblicato online: 06 lug 2022

Pagine: 32 - 38

DOI: https://doi.org/10.2478/kbo-2022-0084

Parole chiaven-th order linear differential equations with constant coefficients, method of variation of constants, general solution, free term in the form () ln

© 2022 Vasile Căruţaşu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following form P(x)^. ln x and the Characteristic Equation Has a Real Root of Order of Multiplicity n

Parole chiave
n-th order linear differential equations with constant coefficients, method of variation of constants, general solution, free term in the form () ln