16 -18 da dt 12 -14 with the initial value -14 z(0) -11 z(t) =
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 of Differential Equations**
We are given the system of differential equations:
\[
\frac{dx}{dt} =
\begin{bmatrix}
16 & -18 \\
12 & -14
\end{bmatrix}
x
\]
**Initial Value**
The initial condition is given by:
\[
x(0) =
\begin{bmatrix}
-14 \\
-11
\end{bmatrix}
\]
**Solution Form**
Determine the function \( x(t) \) that satisfies the system with the initial condition:
\[
x(t) =
\begin{bmatrix}
\text{Enter solution for } x_1(t) \\
\text{Enter solution for } x_2(t)
\end{bmatrix}
\]
*Note*: The solution involves finding the general form of \( x(t) \) which consists of solving the matrix exponential based upon the provided matrix, and then applying the initial conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56661073-d5cb-4d6d-af43-dff77ec9898b%2Fd767d6d7-402e-46ff-a669-826b83de4916%2Fez2gq3h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the System of Differential Equations**
We are given the system of differential equations:
\[
\frac{dx}{dt} =
\begin{bmatrix}
16 & -18 \\
12 & -14
\end{bmatrix}
x
\]
**Initial Value**
The initial condition is given by:
\[
x(0) =
\begin{bmatrix}
-14 \\
-11
\end{bmatrix}
\]
**Solution Form**
Determine the function \( x(t) \) that satisfies the system with the initial condition:
\[
x(t) =
\begin{bmatrix}
\text{Enter solution for } x_1(t) \\
\text{Enter solution for } x_2(t)
\end{bmatrix}
\]
*Note*: The solution involves finding the general form of \( x(t) \) which consists of solving the matrix exponential based upon the provided matrix, and then applying the initial conditions.
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