On ( Semi Homogeneous Systems of Differential Equations
DOI:
https://doi.org/10.21123/bsj.2024.9552Keywords:
δ-semi- homogeneous system, Jacobean matrix, J-semi- homogeneous system, Semi-homogenous, System of differential equationsAbstract
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.
Received 22/09/2023
Revised 03/03/2024
Accepted 05/03/2024
Published Online First 20/09/2024
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Copyright (c) 2024 Aya H. Hasan, Bassam Jabbar AL-Asadi AL-Asadi
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