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Consider the system of differential equations Y₁ 8y1 - 4y2, y₂ = 10y₁-4y2. =

Consider the system of differential equations Y₁ 8y1 - 4y2, y₂ = 10y₁-4y2. =

Advanced Engineering Mathematics
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 \( y_2 \).
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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