Linear Algebra with Differential Equations/Heterogeneous Linear Differential Equations

Introduction

We now tackle the problem of $\mathbf{G}(t)$ being nonzero, so that we have the following problem:

$\mathbf{X}' = \mathbf{AX} + \mathbf{G}(t)$

There are four reasonable ways to solve this.

• Diagonalization
• Method of Undetermined Coefficients
• Variation of Parameters
• Laplacian Transforms