Advanced Engineering Mathematics, 7th Edition

10.2 Homogeneous Linear Systems

INTRODUCTION

In Example 7 of Section 10.1 we saw that the general solution of the homogeneous system X′ = X is X = c₁X₁ + . Since both solution vectors have the form X_i = , i = 1, 2, where k₁, k₂, λ₁, and λ₂ are constants, we are prompted to ask whether we can always find a solution of the form

X = e^λt = Ke^λt(1)