Find a real general solution of the system d -8 -3 dt \y 3 -2
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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![**Linear System of Differential Equations**
**Problem Statement:**
Find a real general solution of the system:
\[
\frac{d}{dt} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -8 & -3 \\ 3 & -2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}
\]
**Explanation:**
This problem involves solving a system of linear differential equations. The system is given in matrix form where the derivative of the vector \((x, y)^T\) is expressed as a product of a matrix with \((x, y)^T\). The matrix involved is:
\[
A = \begin{pmatrix} -8 & -3 \\ 3 & -2 \end{pmatrix}
\]
The goal is to find the general solution for the variables \(x(t)\) and \(y(t)\). The system can be solved using methods such as eigenvalue-eigenvector analysis or diagonalization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F107751dd-22a7-4c13-a90b-ff8221b081c3%2F5bd494cd-1062-4a24-98e3-6efe4abc8e9a%2F78tcg5_processed.png&w=3840&q=75)
Transcribed Image Text:**Linear System of Differential Equations**
**Problem Statement:**
Find a real general solution of the system:
\[
\frac{d}{dt} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -8 & -3 \\ 3 & -2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}
\]
**Explanation:**
This problem involves solving a system of linear differential equations. The system is given in matrix form where the derivative of the vector \((x, y)^T\) is expressed as a product of a matrix with \((x, y)^T\). The matrix involved is:
\[
A = \begin{pmatrix} -8 & -3 \\ 3 & -2 \end{pmatrix}
\]
The goal is to find the general solution for the variables \(x(t)\) and \(y(t)\). The system can be solved using methods such as eigenvalue-eigenvector analysis or diagonalization.
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