i 3 5х + 10у ý = -x – y —х —
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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Find the eigenvalues and eigenvectors.
I know the eigenvalues are 2+i and 2-i.
![The image displays a system of differential equations:
\[
\begin{aligned}
\dot{x} &= 5x + 10y \\
\dot{y} &= -x - y
\end{aligned}
\]
This system consists of two first-order linear differential equations involving the variables \( x \) and \( y \). The dot notation (\(\dot{x}\), \(\dot{y}\)) represents the derivatives of \( x \) and \( y \) with respect to time, commonly used in dynamic systems to denote rates of change.
These equations might be analyzed to study the stability and behavior of the system, often involving eigenvalues and eigenvectors to understand the nature of solutions such as equilibrium points, oscillations, or decay.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88e1e2e4-888b-4182-8c02-fd46dda7f6b1%2F4071b473-c18b-43d6-9a4e-8fbed86085cd%2Fv4apzx4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a system of differential equations:
\[
\begin{aligned}
\dot{x} &= 5x + 10y \\
\dot{y} &= -x - y
\end{aligned}
\]
This system consists of two first-order linear differential equations involving the variables \( x \) and \( y \). The dot notation (\(\dot{x}\), \(\dot{y}\)) represents the derivatives of \( x \) and \( y \) with respect to time, commonly used in dynamic systems to denote rates of change.
These equations might be analyzed to study the stability and behavior of the system, often involving eigenvalues and eigenvectors to understand the nature of solutions such as equilibrium points, oscillations, or decay.
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