3. Write the given system of differential equations in the matrix form and find exponential solutions of the system. = - 4x2 (a) { 1/2 = 821-752 (c) { x' = 3x + 2y y' = 6x + 4y x' = x + 6y y' = 5x + 2y (b) { ; (d) x₁ ម 11213 || || || = I1 x2 + x3 +3 x1 + x2
3. Write the given system of differential equations in the matrix form and find exponential solutions of the system. = - 4x2 (a) { 1/2 = 821-752 (c) { x' = 3x + 2y y' = 6x + 4y x' = x + 6y y' = 5x + 2y (b) { ; (d) x₁ ម 11213 || || || = I1 x2 + x3 +3 x1 + x2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
A, B, D please
![**Exercise 3:**
Write the given system of differential equations in matrix form and find exponential solutions of the system.
**Equations:**
(a)
\[
\begin{cases}
\dot{x}_1 = 5x_1 - 4x_2 \\
\dot{x}_2 = 8x_1 - 7x_2
\end{cases}
\]
(b)
\[
\begin{cases}
\dot{x} = x + 6y \\
\dot{y} = 5x + 2y
\end{cases}
\]
(c)
\[
\begin{cases}
\dot{y} = 3x + 2y \\
x' = 6x + 4y
\end{cases}
\]
(d)
\[
\begin{cases}
x'_3 = x_2 + x_3 \\
x'_2 = x_1 + x_2 \\
x'_1 = x_2 + x_1
\end{cases}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F801d34df-dcab-45aa-85e0-2349cce424a4%2F670c4c16-8232-454d-b257-5ceb2c8fd60d%2F6fbz2sg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 3:**
Write the given system of differential equations in matrix form and find exponential solutions of the system.
**Equations:**
(a)
\[
\begin{cases}
\dot{x}_1 = 5x_1 - 4x_2 \\
\dot{x}_2 = 8x_1 - 7x_2
\end{cases}
\]
(b)
\[
\begin{cases}
\dot{x} = x + 6y \\
\dot{y} = 5x + 2y
\end{cases}
\]
(c)
\[
\begin{cases}
\dot{y} = 3x + 2y \\
x' = 6x + 4y
\end{cases}
\]
(d)
\[
\begin{cases}
x'_3 = x_2 + x_3 \\
x'_2 = x_1 + x_2 \\
x'_1 = x_2 + x_1
\end{cases}
\]
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