Solve the system dx dt x(0) = = -22 18 with the initial value 1 x(t) = -27 23 2 8
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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Question
![**Solve the System**
\[
\frac{dx}{dt} =
\begin{bmatrix}
-22 & 18 \\
-27 & 23
\end{bmatrix}
x
\]
**with the initial value**
\[
x(0) =
\begin{bmatrix}
1 \\
2
\end{bmatrix}
.
\]
\[
x(t) =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
.
\]
**Description:**
This system represents a set of first-order linear differential equations with a given initial condition. The task is to solve for \( x(t) \), the state vector as a function of time \( t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6890296c-2fc0-4a83-b66a-ee1a85d807a1%2Faa093f62-7891-4bd5-a4c9-60d59398d4de%2Fecdv4pf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the System**
\[
\frac{dx}{dt} =
\begin{bmatrix}
-22 & 18 \\
-27 & 23
\end{bmatrix}
x
\]
**with the initial value**
\[
x(0) =
\begin{bmatrix}
1 \\
2
\end{bmatrix}
.
\]
\[
x(t) =
\begin{bmatrix}
\Box \\
\Box
\end{bmatrix}
.
\]
**Description:**
This system represents a set of first-order linear differential equations with a given initial condition. The task is to solve for \( x(t) \), the state vector as a function of time \( t \).
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