ABSTRACT
This chapter considers a system of coupled first order differential equations (ODE). Most of the modern computer software for solving ODEs, especially nonlinear ODEs, is formulated as a system of first order ODE. The chapter deals with the linear system of ODEs for which analytic solutions can be obtained. For nonlinear ODEs, a more advanced perturbation method for studying the stability of the evolving systems of ODEs focuses mainly on the first order ODE system. The chapter shows how systems of ODE of arbitrary order and with an arbitrary number of unknowns are transformed into a system of first order ODEs. It summarizes the uncoupling of ODEs for multiple unknowns involving higher derivatives originated by Jacobi and Chrystal. The chapter presents solution of ODE system with constant coefficients in the context of a matrix eigenvalue problem. It discusses the solution technique for solving a system of first order ODE.
