3.1 Theory of Linear Equations

3.2 Reduction of Order

3.3 Linear Equations with Constant Coefficients

3.4 Undetermined Coefficients

3.5 Variation of Parameters

3.6 Cauchy–Euler Equations

3.7 Nonlinear Equations

3.8 Linear Models: Initial-Value Problems

3.9 Linear Models: Boundary-Value Problems

3.10 Green’s Functions

3.11 Nonlinear Models

3.12 Solving Systems of Linear DEs

Chapter 3 in Review

We turn now to differential equations of order two or higher. In the first six sections of this chapter we examine the underlying theory and solution methods for certain kinds of linear DEs. The difficulties that surround higher-order nonlinear DEs and the few methods for solving such equations are examined next (Section 3.7). The chapter concludes with higher-order linear and nonlinear mathematical models (Sections 3.8, 3.9, and 3.11) and the first of several methods on how to solve systems of linear DEs (Section 3.12).