Find a particular solution of the indicated linear system that satisfies the initial conditions x, (0) = 6, X2 (0) = - 9. 7 X' = - 2 5t - 5t x; x = e X2 = e 12 - 7 ..... The particular solution is x, (t) = and x2(t) =
Find a particular solution of the indicated linear system that satisfies the initial conditions x, (0) = 6, X2 (0) = - 9. 7 X' = - 2 5t - 5t x; x = e X2 = e 12 - 7 ..... The particular solution is x, (t) = and x2(t) =
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 Statement:**
Find a particular solution of the indicated linear system that satisfies the initial conditions \( x_1(0) = 6 \), \( x_2(0) = -9 \).
**System of Equations:**
\[
x' =
\begin{bmatrix}
7 & -2 \\
12 & -7
\end{bmatrix}
x, \quad
x_1 = e^{5t}
\begin{bmatrix}
1 \\
1
\end{bmatrix}, \quad
x_2 = e^{-5t}
\begin{bmatrix}
1 \\
6
\end{bmatrix}
\]
**Task:**
Find the particular solution for \( x_1(t) \) and \( x_2(t) \) that meets the initial conditions:
- \( x_1(0) = 6 \)
- \( x_2(0) = -9 \)
**Solution Format:**
- \( x_1(t) = \) [Input field]
- \( x_2(t) = \) [Input field]
**Instructions:**
Using the given system of equations and the initial conditions, determine the particular solutions for \( x_1(t) \) and \( x_2(t) \) and input your solutions in the respective fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b9e86b7-74ce-4a31-bbac-c9b385fe1b9d%2F079021d0-894e-432c-8024-580116dca67d%2Fx5g2e3_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 \( x_1(0) = 6 \), \( x_2(0) = -9 \).
**System of Equations:**
\[
x' =
\begin{bmatrix}
7 & -2 \\
12 & -7
\end{bmatrix}
x, \quad
x_1 = e^{5t}
\begin{bmatrix}
1 \\
1
\end{bmatrix}, \quad
x_2 = e^{-5t}
\begin{bmatrix}
1 \\
6
\end{bmatrix}
\]
**Task:**
Find the particular solution for \( x_1(t) \) and \( x_2(t) \) that meets the initial conditions:
- \( x_1(0) = 6 \)
- \( x_2(0) = -9 \)
**Solution Format:**
- \( x_1(t) = \) [Input field]
- \( x_2(t) = \) [Input field]
**Instructions:**
Using the given system of equations and the initial conditions, determine the particular solutions for \( x_1(t) \) and \( x_2(t) \) and input your solutions in the respective fields.
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