Consider the initial value problem dx 4 dt X₁ 1 x(t) = (a) Find the eigenvalues and eigenvectors for the coefficient matrix. [8] 7₁ = = 7¹x₁ X, " x(0) = and X₂ = - V2 = (b) Solve the initial value problem. Give your solution in real form. (181
Consider the initial value problem dx 4 dt X₁ 1 x(t) = (a) Find the eigenvalues and eigenvectors for the coefficient matrix. [8] 7₁ = = 7¹x₁ X, " x(0) = and X₂ = - V2 = (b) Solve the initial value problem. Give your solution in real form. (181
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Consider the initial value problem
dx 4
dt
X₁
1
x(t) =
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
[18]
7₁
=
=
7¹x₁
X,
"
and X₂
x(0) =
=
-
An ellipse with clockwise orientation
Describe the trajectory.
V2
(b) Solve the initial value problem. Give your solution in real form.
18
=
8
Use the phase plotter pplane9.m in MATLAB to answer the following question.
1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F070af868-609a-41f9-8688-eb3f6e6f6d34%2Fa5ca16df-978e-4d24-bc86-01898ac01b35%2Fqif4z8n_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
dx 4
dt
X₁
1
x(t) =
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
[18]
7₁
=
=
7¹x₁
X,
"
and X₂
x(0) =
=
-
An ellipse with clockwise orientation
Describe the trajectory.
V2
(b) Solve the initial value problem. Give your solution in real form.
18
=
8
Use the phase plotter pplane9.m in MATLAB to answer the following question.
1.
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