.x'= = (² 3 -2 x, x(0) = 3 (²);
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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![### Problem 13
**Objective:** In each of Problems 13 through 16, solve the given initial value problem. Draw component plots of \(x_1\) and \(x_2\) versus \(t\). Describe the behavior of the solution as \( t \to \infty \).
Consider the system described in Problem 13:
\[ \mathbf{x}' = \begin{pmatrix} 1 & -2 \\ 3 & -4 \end{pmatrix} \mathbf{x}, \quad \mathbf{x}(0) = \begin{pmatrix} 3 \\ 1 \end{pmatrix}; \]
Refer to Problem 2 for further details.
**Instructions:**
1. Solve the initial value problem provided.
2. Plot the components \(x_1\) and \(x_2\) as functions of time \(t\).
3. Describe the behavior of the solution as \( t \to \infty \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3632b9ca-0e22-48c8-943d-c9e08fc0f04c%2F89a0d0d7-abbf-452e-aa6c-64a9849dd685%2F7dz5w4c_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 13
**Objective:** In each of Problems 13 through 16, solve the given initial value problem. Draw component plots of \(x_1\) and \(x_2\) versus \(t\). Describe the behavior of the solution as \( t \to \infty \).
Consider the system described in Problem 13:
\[ \mathbf{x}' = \begin{pmatrix} 1 & -2 \\ 3 & -4 \end{pmatrix} \mathbf{x}, \quad \mathbf{x}(0) = \begin{pmatrix} 3 \\ 1 \end{pmatrix}; \]
Refer to Problem 2 for further details.
**Instructions:**
1. Solve the initial value problem provided.
2. Plot the components \(x_1\) and \(x_2\) as functions of time \(t\).
3. Describe the behavior of the solution as \( t \to \infty \).
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