Systems of Differential Equations

Uri Elias ()
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Uri Elias: Technion – Israel Institute of Technology, Department of Mathematics

Chapter Chapter 5 in Fundamentals of Ordinary Differential Equations, 2025, pp 159-197 from Springer

Abstract: Abstract Existence, uniqueness, and stability are defined for arbitrary systems of equations, but later, only linear systems are studied. Vector and matrix notation is used, and the study of independence, spanning, bases, and Wronskian and Abel’s formula is almost a copy and paste of the corresponding results in Chap. 3 . This leads to the fundamental matrix of a system. Systems with constant coefficients are easy to solve when the system has a full set of eigenvectors. For systems that have no basis of eigenvectors, we describe (without proof) its Jordan canonical form and develop a basis of vector solutions. Jordan chains appear naturally. Non-homogeneous systems are solved by variations of parameters and the fundamental matrix.

Date: 2025
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DOI: 10.1007/978-3-031-86532-9_5

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