Chapter 5.2, Problem 2E

Interpretation Introduction

Interpretation:

A of the system $\dot{\text{x}}\text{ = x - y}$, $\dot{\text{y}}\text{ = x + y}$ is to be found and it has eigenvalues ${\text{λ}}_{\text{1}}{\text{=1 - i and λ}}_{\text{2}}\text{=1 + i}$ is to be shown. Also, $\text{x(t)}$ in terms of real valued functions is to be expressed.

Concept Introduction:

Equations for two dimensional linear system are $\dot{\text{x}}\text{ = ax + by}$, $\dot{\text{y}}\text{ = cx + dy}$.

The above linear system is expressed in the form $\dot{\text{x}}\text{ = Ax}$.

The standard characteristics polynomials is

${\text{λ}}^{\text{2}}\text{- τλ + Δ = 0}$, where $\text{τ}$ is trace of matrix A, $\text{λ}$ is corresponding eigenvalue, and $\text{Δ}$ is the determinant of matrix A.