Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0) = 5, x₂ (0)=2, and x3 (0) = 6. -13-17 -2 3 3t x' = 10 14 2 x X₁5 -2.x₂ 04 - 10 - 10 2 2 The particular solution is x₁ (t) = x₂(t)=, and x3 (t) =
Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0) = 5, x₂ (0)=2, and x3 (0) = 6. -13-17 -2 3 3t x' = 10 14 2 x X₁5 -2.x₂ 04 - 10 - 10 2 2 The particular solution is x₁ (t) = x₂(t)=, and x3 (t) =
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
![**Problem Statement:**
Find a particular solution of the indicated linear system that satisfies the initial conditions \(x_1(0) = 5\), \(x_2(0) = 2\), and \(x_3(0) = 6\).
\[ \mathbf{x'} = \begin{bmatrix} -13 & -17 & -2 \\ 10 & 14 & 2 \\ -10 & -10 & 2 \end{bmatrix} \mathbf{x}; \quad \mathbf{x_1} = e^{-3t} \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix}, \quad \mathbf{x_2} = e^{2t} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \quad \mathbf{x_3} = e^{4t} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} \]
---
**Diagram Explanation:**
1. **Initial Conditions and Given Matrices:**
- A 3x3 coefficient matrix in the differential equation \( \mathbf{x'} \).
- Three linearly independent solutions:
- \( \mathbf{x_1} = e^{-3t} \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix} \)
- \( \mathbf{x_2} = e^{2t} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \)
- \( \mathbf{x_3} = e^{4t} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} \)
2. **Particular Solution to Find:**
- The particular solution must satisfy the given initial conditions: \(x_1(0) = 5\), \(x_2(0) = 2\), and \(x_3(0) = 6\).
---
**Solution Format:**
The particular solution is:
\[ x_1(t) = \_\_\_\_ \]
\[ x_2(t) = \_\_\_\_ \]
\[ x_3(t) = \_\_\_\_ \]
Please enter the specific solutions for \(x_1(t)\), \(x_2(t)\), and \(x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06bbd155-c9d1-4bdc-8881-0cd893ac016a%2F5369c459-b4bb-4861-8019-70520a08fdb6%2F121c5rb_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a particular solution of the indicated linear system that satisfies the initial conditions \(x_1(0) = 5\), \(x_2(0) = 2\), and \(x_3(0) = 6\).
\[ \mathbf{x'} = \begin{bmatrix} -13 & -17 & -2 \\ 10 & 14 & 2 \\ -10 & -10 & 2 \end{bmatrix} \mathbf{x}; \quad \mathbf{x_1} = e^{-3t} \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix}, \quad \mathbf{x_2} = e^{2t} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \quad \mathbf{x_3} = e^{4t} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} \]
---
**Diagram Explanation:**
1. **Initial Conditions and Given Matrices:**
- A 3x3 coefficient matrix in the differential equation \( \mathbf{x'} \).
- Three linearly independent solutions:
- \( \mathbf{x_1} = e^{-3t} \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix} \)
- \( \mathbf{x_2} = e^{2t} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \)
- \( \mathbf{x_3} = e^{4t} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} \)
2. **Particular Solution to Find:**
- The particular solution must satisfy the given initial conditions: \(x_1(0) = 5\), \(x_2(0) = 2\), and \(x_3(0) = 6\).
---
**Solution Format:**
The particular solution is:
\[ x_1(t) = \_\_\_\_ \]
\[ x_2(t) = \_\_\_\_ \]
\[ x_3(t) = \_\_\_\_ \]
Please enter the specific solutions for \(x_1(t)\), \(x_2(t)\), and \(x
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)