Solve the IVP dx dt [ x(t) = 12 0 X, -24 0 x(0) = [13] 181
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
![**Problem Statement:**
Solve the Initial Value Problem (IVP) given by the system of differential equations:
\[
\frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x}
\]
with the initial condition:
\[
\mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix}
\]
**Solution Form:**
The solution vector \(\mathbf{x}(t)\) is expressed as:
\[
\mathbf{x}(t) = \begin{bmatrix} \Box \\ \Box \end{bmatrix}
\]
where the boxes represent the functions or constants that need to be determined as part of solving this system of differential equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ab47578-81e4-46a2-abcb-43bbb3318efe%2F98ad3357-8234-4304-ad72-0ff4845ed22b%2Fl1kvbrr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the Initial Value Problem (IVP) given by the system of differential equations:
\[
\frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x}
\]
with the initial condition:
\[
\mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix}
\]
**Solution Form:**
The solution vector \(\mathbf{x}(t)\) is expressed as:
\[
\mathbf{x}(t) = \begin{bmatrix} \Box \\ \Box \end{bmatrix}
\]
where the boxes represent the functions or constants that need to be determined as part of solving this system of differential equations.
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