SECTION 7 - Linear Systems with Constant Coefficients

Abstract

This chapter discusses the linear systems with constant coefficients. Every nth-order differential equation can be reduced to a system of n first-order differential equations. The solution of the systems of linear differential equations is similar to the solutions of linear equations of arbitrary order. The techniques of computing solutions require results from linear algebra. It follows by the fundamental existence theorem that the system has a fundamental system of solutions and that every other solution is a linear combination of the fundamental solution. In the case of multiple eigenvalues, there are a number of independent solutions of the equation corresponding to the multiplicity of each of the eigenvalues.