Solve the system -18 21 da dt -14 17 with the initial value 10 æ (0) ||
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 Statement**
**Solve the system**
\[
\frac{dx}{dt} =
\begin{bmatrix}
-18 & 21 \\
-14 & 17
\end{bmatrix}
x
\]
**with the initial value**
\[
x(0) =
\begin{bmatrix}
10 \\
5
\end{bmatrix}
.
\]
**Find**
\[
x(t) =
\begin{bmatrix}
\text{(enter solution here)} \\
\text{(enter solution here)}
\end{bmatrix}
.
\]
**Explanation**
The problem requires solving a system of linear differential equations using a given matrix and an initial value. The matrix used in the system is a 2x2 matrix with entries \(-18\), \(21\), \(-14\), and \(17\). The initial condition is provided as a vector with values \(10\) and \(5\). The goal of the exercise is to compute the solution vector \(x(t)\) for this system, which should be entered in the provided space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb738ee4b-0d92-438d-b96f-d8d02fb325c0%2F2920f1db-74f6-468d-8c62-73d17633b0da%2Fg0w03ra_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
**Solve the system**
\[
\frac{dx}{dt} =
\begin{bmatrix}
-18 & 21 \\
-14 & 17
\end{bmatrix}
x
\]
**with the initial value**
\[
x(0) =
\begin{bmatrix}
10 \\
5
\end{bmatrix}
.
\]
**Find**
\[
x(t) =
\begin{bmatrix}
\text{(enter solution here)} \\
\text{(enter solution here)}
\end{bmatrix}
.
\]
**Explanation**
The problem requires solving a system of linear differential equations using a given matrix and an initial value. The matrix used in the system is a 2x2 matrix with entries \(-18\), \(21\), \(-14\), and \(17\). The initial condition is provided as a vector with values \(10\) and \(5\). The goal of the exercise is to compute the solution vector \(x(t)\) for this system, which should be entered in the provided space.
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