#1 = x₂ = x3 = Solve the following initial value problem: 7= 3 -5 1 -1 6 7 -1 8 6 7, 7(0) = 4 3
#1 = x₂ = x3 = Solve the following initial value problem: 7= 3 -5 1 -1 6 7 -1 8 6 7, 7(0) = 4 3
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
![### Solve the following initial value problem:
Given the initial value problem:
\[ \frac{d \vec{x}}{dt} = \begin{pmatrix} 3 & -1 & 6 \\ -5 & 7 & 6 \\ 1 & -1 & 8 \end{pmatrix} \vec{x}, \quad \vec{x}(0) = \begin{pmatrix} 6 \\ 4 \\ 3 \end{pmatrix} \]
Find the solutions:
\[ x_1 = \]
\[ x_2 = \]
\[ x_3 = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F216015d9-daff-4e98-b3d1-7f3f5202e820%2F05324428-15e9-4c1b-813c-54c7fcf9ef7e%2Fiarelad_processed.png&w=3840&q=75)
Transcribed Image Text:### Solve the following initial value problem:
Given the initial value problem:
\[ \frac{d \vec{x}}{dt} = \begin{pmatrix} 3 & -1 & 6 \\ -5 & 7 & 6 \\ 1 & -1 & 8 \end{pmatrix} \vec{x}, \quad \vec{x}(0) = \begin{pmatrix} 6 \\ 4 \\ 3 \end{pmatrix} \]
Find the solutions:
\[ x_1 = \]
\[ x_2 = \]
\[ x_3 = \]
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