Consider the system of differential equations Y₁ 8y1 - 4y2, y₂ = 10y₁-4y2. =
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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a) Rewrite this system as a matrix equation y ′=Ay
b) Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list.
![Consider the system of differential equations
\[
\begin{align*}
y_1' &= 8y_1 - 4y_2, \\
y_2' &= 10y_1 - 4y_2.
\end{align*}
\]
This system represents two first-order linear differential equations, where \( y_1' \) and \( y_2' \) denote the derivatives of \( y_1 \) and \( y_2 \) with respect to an independent variable, typically time. The equations are coupled as they contain both \( y_1 \) and \( y_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2Fbc4daef5-2658-40d5-b24f-27fe7d733e3e%2F1ncqcq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
\[
\begin{align*}
y_1' &= 8y_1 - 4y_2, \\
y_2' &= 10y_1 - 4y_2.
\end{align*}
\]
This system represents two first-order linear differential equations, where \( y_1' \) and \( y_2' \) denote the derivatives of \( y_1 \) and \( y_2 \) with respect to an independent variable, typically time. The equations are coupled as they contain both \( y_1 \) and \( y_2 \).
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