# Higher-Order Linear Differential Equations

• Clay C. Ross
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Linear differential equations of higher order have useful and interesting applications, just as first-order differential equations do. We study linear differential equations of higher order in this chapter. The word linear in the chapter title should suggest that techniques for solving linear equations will be important. What is somewhat unexpected is that we have to appeal to the theory of solving polynomial equations in one variable. Though the solution technique for first-order equations gave us a complete solution in essentially one step, this is not the case here. For the first time we have to solve the homogeneous and nonhomogeneous equations separately and by different methods.

## Keywords

Characteristic Polynomial Constant Coefficient Linear Differential Equation Independent Solution Linear Differential Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.