Problem 7.3: Find the GS of 1 ()' = ( ²3 ) ( ) -3
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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![**Problem 7.3:** Find the GS of
\[
\begin{pmatrix}
x' \\
y'
\end{pmatrix}
=
\begin{pmatrix}
1 & 3 \\
-3 & 7
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
\]
**Explanation:**
- The problem involves finding the general solution (GS) of a system of differential equations represented in matrix form.
- The left-hand side of the equation shows the derivative of a vector \(\begin{pmatrix} x' \\ y' \end{pmatrix}\).
- The right-hand side consists of a matrix \(\begin{pmatrix} 1 & 3 \\ -3 & 7 \end{pmatrix}\) multiplied by a vector \(\begin{pmatrix} x \\ y \end{pmatrix}\).
- This is a typical setup for solving a system of linear first-order differential equations using matrix methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2Fae065e95-9c39-4314-922c-917dc0fda7a0%2Fyh6z93g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7.3:** Find the GS of
\[
\begin{pmatrix}
x' \\
y'
\end{pmatrix}
=
\begin{pmatrix}
1 & 3 \\
-3 & 7
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
\]
**Explanation:**
- The problem involves finding the general solution (GS) of a system of differential equations represented in matrix form.
- The left-hand side of the equation shows the derivative of a vector \(\begin{pmatrix} x' \\ y' \end{pmatrix}\).
- The right-hand side consists of a matrix \(\begin{pmatrix} 1 & 3 \\ -3 & 7 \end{pmatrix}\) multiplied by a vector \(\begin{pmatrix} x \\ y \end{pmatrix}\).
- This is a typical setup for solving a system of linear first-order differential equations using matrix methods.
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