Solution Found!
In Exercises 7 and 8, make a change of variable that
Chapter 5, Problem 7E(choose chapter or problem)
Problem 7E
In Exercises 7 and 8, make a change of variable that decouples the equation . Write the equation and show the calculation that leads to the uncoupled system specifying P and D.
A as in Exercise 5
Reference:
In Exercises 3–6, solve the initial value problem for . Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by .Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.
Questions & Answers
QUESTION:
Problem 7E
In Exercises 7 and 8, make a change of variable that decouples the equation . Write the equation and show the calculation that leads to the uncoupled system specifying P and D.
A as in Exercise 5
Reference:
In Exercises 3–6, solve the initial value problem for . Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by .Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.
ANSWER:
Solution 7E
Step 1 of 5
Consider the differential equation where,
.
The objective is to write the decoupled equation as uncoupled system .
First it is need to find the matrices such that .
Find the characteristic polynomial of the matrix :
Therefore, the eigenvalues of are 4, 6.
