Abstract
The concept of homogeneity in differential equations can be generalized to systems of differential equations as shown in this work. The classification of three-dimensional differential equation systems is presented based on the definition of the Jacobean matrix and its determinant, where two systems of the homogeneous system are defined, called the J-semi-homogeneous system and the other δ-semi-homogeneous system, where the first definition is based on the Jacobian matrix, while the second is based on the determinant of the Jacobite matrix. Examples are given for both definitions, and the relationship between the two definitions will be studied. In addition to finding an equivalent for these two definitions, some results for these two definitions have also been proven.
Keywords
δ-semi-homogeneous system, Jacobean matrix, J-semi-homogeneous system, Semi-homogenous, System of differential equations
Subject Area
Mathematics
First Page
646
Last Page
663
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Receive Date
9-22-2023
Revise Date
3-3-2024
Accept Date
3-5-2024
How to Cite this Article
Hasan, Aya H. and AL-Asadi, Bassam Jabbar
(2025)
"On (J - δ) Semi Homogeneous Systems of Differential Equations,"
Baghdad Science Journal: Vol. 22:
Iss.
2, Article 24.
DOI: https://doi.org/10.21123/bsj.2024.9552
