Consider the Initial Value Problem: x₁ = x2 X₁ = v1 = x2 = 2x1 + 2x2 - 4x1 - 2x₂¹ (a) Find the eigenvalues and eigenvectors for the coefficient matrix. [8] x1 (0) x2 (0) = 4 = 6 , and X₂ = v₂ = (b) Solve the initial value problem. Give your solution in real form. x1 An ellipse with clockwise orientation phase plotter pplane9.m in MATLAB to describe the trajectory. [18] î 1. Use the
Consider the Initial Value Problem: x₁ = x2 X₁ = v1 = x2 = 2x1 + 2x2 - 4x1 - 2x₂¹ (a) Find the eigenvalues and eigenvectors for the coefficient matrix. [8] x1 (0) x2 (0) = 4 = 6 , and X₂ = v₂ = (b) Solve the initial value problem. Give your solution in real form. x1 An ellipse with clockwise orientation phase plotter pplane9.m in MATLAB to describe the trajectory. [18] î 1. Use the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the Initial Value Problem:
\[
\begin{aligned}
x_1' & = 2x_1 + 2x_2 \quad & x_1(0) = 4 \\
x_2' & = -4x_1 - 2x_2 \quad & x_2(0) = 6 \\
\end{aligned}
\]
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
\[
\lambda_1 = \Box, \quad \vec{v}_1 =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
, \quad \text{and} \quad \lambda_2 = \Box, \quad \vec{v}_2 =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
\]
(b) Solve the initial value problem. Give your solution in real form.
\[
\begin{aligned}
x_1 = \Box, \\
x_2 = \Box.
\end{aligned}
\]
An ellipse with clockwise orientation. Use the phase plotter pplane9.m in MATLAB to describe the trajectory.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6890296c-2fc0-4a83-b66a-ee1a85d807a1%2Fd349676f-1869-4866-9076-a3874a74f1e7%2Fd2fwm5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the Initial Value Problem:
\[
\begin{aligned}
x_1' & = 2x_1 + 2x_2 \quad & x_1(0) = 4 \\
x_2' & = -4x_1 - 2x_2 \quad & x_2(0) = 6 \\
\end{aligned}
\]
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
\[
\lambda_1 = \Box, \quad \vec{v}_1 =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
, \quad \text{and} \quad \lambda_2 = \Box, \quad \vec{v}_2 =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
\]
(b) Solve the initial value problem. Give your solution in real form.
\[
\begin{aligned}
x_1 = \Box, \\
x_2 = \Box.
\end{aligned}
\]
An ellipse with clockwise orientation. Use the phase plotter pplane9.m in MATLAB to describe the trajectory.
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