4 - Higher-Order Differential Equations

Abstract

This chapter discusses several methods for solving higher-order differential equations with constant coefficients. To develop the methods needed to solve higher-order differential equations, several important defirutions and theorems are needed, such as nth-order ordinary linear differenüal equation, linearly dependent and linearly independent, and wronskian. Obtaining a collection of n linearly independent solutions to an nth-order linear differential equation is of great importance in solving equations of fundamental set of solutions. The chapter explains that the linear combination of the functions in a fundamental set of solutions of an nth-order homogeneous linear differential equation is also a solution of the differential equation. The solutions of any nth-order homogeneous linear differential equation with constant coefficients are determined by the solutions of the characteristic equation.