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CHAPTER 10
Systems of Linear Differential Equations
10.2 Homogeneous Linear Systems
10.3 Solution by Diagonalization
10.4 Nonhomogeneous Linear Systems
We encountered systems of ordinary differential equations in Sections 2.9, 3.12, and 4.6 and were able to solve some systems using either systematic elimination or the Laplace transform. In this chapter we focus only on systems of linear first-order differential equations. We will see that the general theory of systems of linear DEs and the solution procedure is similar to that of linear higher-order equations considered in Chapter 3. This material is fundamental to the analysis of systems of nonlinear first-order equations in Chapter 11. Matrix notation and properties are used extensively throughout this chapter. If you are unfamiliar with these concepts, a review of Chapter 8 is recommended.