Fundamental systems of solutions of some linear differential equations of higher order
-
Jozef Fecenko
Abstract
The article deals with the issue of the existence of fundamental systems for solving some types of homogeneous linear differential equations with constant coefficients, which are created using higher derivatives of the so-called fundamental function. The first part of the article also partially expands on new information from the article [4]. Some interesting results are presented: Let f(x) = xn−1 sin βx be the fundamental function of the solutions to the differential equation
(Communicated by Michal Fec̆kan)
References
[1] ChatGPT: (artificial intelligence) https://chat.openai.com.Search in Google Scholar
[2] Collective of authors: Applied Mathematics I, II, SNTL, Publishing House of Technical Literature, Prague 1978 (in Czech).Search in Google Scholar
[3] Fecenko, J.: Matrix differential operator method of finding a particular solution to a nonhomogeneous linear ordinary differential equation with constant coefficients, https://arxiv.org/abs/2101.02037.Search in Google Scholar
[4] Fecenko, J.: Other fundamental systems of solutions of the differential equation (D2−2αD+α2+β2ny = 0 β ≠ 0, Math. Slovaca 74(5) (2024), 1155–1164.10.1515/ms-2024-0083Search in Google Scholar
[5] Fecenko, J.—Diekema, E.: On the linear (in)dependence of sequences of derivatives of the functions xn sin x and xn cos x, http://arxiv.org/abs/2305.11184Search in Google Scholar
[6] Fecenko, J.—Chalmovianská, J.: Note on the fundamental sets of solution to the differential equations (D2 − 2Dα + α2 ± β2y = 0, Math. Slovaca 74(6) (2024), 1433–1444.10.1515/ms-2024-0103Search in Google Scholar
[7] Gatto, L.—Scherbak, I.: On Generalized Wronskians, https://www.impan.pl/~pragacz/gatto2.pdf.Search in Google Scholar
[8] Spiegel, M. R.: Schaum’s Outline of Theory and Problems of Advanced Mathematics for Engineers and Scientists, McGraw-Hill, 2002.Search in Google Scholar
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
