16 -18 da dt 12 -14 with the initial value -14 x(0) -11 a(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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![To solve the system of differential equations, we start with:
\[
\frac{dx}{dt} = \begin{bmatrix} 16 & -18 \\ 12 & -14 \end{bmatrix} x
\]
with the initial value condition:
\[
x(0) = \begin{bmatrix} -14 \\ -11 \end{bmatrix}
\]
To find the function \( x(t) \), we need to calculate:
\[
x(t) = \begin{bmatrix} \text{[Enter solution for first component]} \\ \text{[Enter solution for second component]} \end{bmatrix}
\]
This equation represents a system of linear differential equations characterized by a matrix containing coefficients for \( x \). The objective is to determine the function \( x(t) \) over time, given the initial state \( x(0) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56661073-d5cb-4d6d-af43-dff77ec9898b%2Fe1007158-1d75-4f4b-8691-9ef622bc390f%2Fypryji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To solve the system of differential equations, we start with:
\[
\frac{dx}{dt} = \begin{bmatrix} 16 & -18 \\ 12 & -14 \end{bmatrix} x
\]
with the initial value condition:
\[
x(0) = \begin{bmatrix} -14 \\ -11 \end{bmatrix}
\]
To find the function \( x(t) \), we need to calculate:
\[
x(t) = \begin{bmatrix} \text{[Enter solution for first component]} \\ \text{[Enter solution for second component]} \end{bmatrix}
\]
This equation represents a system of linear differential equations characterized by a matrix containing coefficients for \( x \). The objective is to determine the function \( x(t) \) over time, given the initial state \( x(0) \).
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