J. Fecenko

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20202023

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math.GM2023

On the linear (in)dependence of sequences of derivatives of the functions $x^{n} sin x$ and $x^{n} cos x$

Jozef Fecenko, Enno Diekema

The main goal of the paper is to prove that the sequence of functions $f (x), D f (x), \dots, D^{2 n + 1} f (x)$ , where $f (x)$ is $x^{n} sin x$ or $x^{n} cos x$ are linearly independent. Or mo…

math.GM2021

Note on the Application of Divergent Series for Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

Jozef Fecenko

There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coef…

math.GM2020

Matrix Differential Operator Method of Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

Jozef Fecenko

The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differentia…

On the linear (in)dependence of sequences of derivatives of the functions xnsinx and xncosx

Note on the Application of Divergent Series for Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

Matrix Differential Operator Method of Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

On the linear (in)dependence of sequences of derivatives of the functions $x^{n} sin x$ and $x^{n} cos x$