Find the general solution of the following systems of differential equation A) 80-180 X' (t) = X (t)
Find the general solution of the following systems of differential equation A) 80-180 X' (t) = X (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
![**Problem Statement:**
Find the general solution of the following systems of differential equations:
**A)**
\[
\vec{X}'(t) = \begin{bmatrix} 1 & -2 \\ 3 & -4 \end{bmatrix} \vec{X}(t)
\]
**B)**
\[
\vec{X}'(t) = \begin{bmatrix} -3 & 2 \\ -1 & -1 \end{bmatrix} \vec{X}(t)
\]
**Explanation:**
Each system of differential equations involves finding the general solution for a vector function \(\vec{X}(t)\). The systems are expressed in matrix form, where \(\vec{X}'(t)\) represents the derivative of the vector \(\vec{X}(t)\) with respect to time \(t\). Each matrix determines the coefficients of the system and influences the behavior of the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ba71b9f-6645-4b82-be5d-cda1c9d5ec57%2F967acb9d-7f35-4f2d-85c6-45ec6b2ef8fe%2Fhbp3si_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the general solution of the following systems of differential equations:
**A)**
\[
\vec{X}'(t) = \begin{bmatrix} 1 & -2 \\ 3 & -4 \end{bmatrix} \vec{X}(t)
\]
**B)**
\[
\vec{X}'(t) = \begin{bmatrix} -3 & 2 \\ -1 & -1 \end{bmatrix} \vec{X}(t)
\]
**Explanation:**
Each system of differential equations involves finding the general solution for a vector function \(\vec{X}(t)\). The systems are expressed in matrix form, where \(\vec{X}'(t)\) represents the derivative of the vector \(\vec{X}(t)\) with respect to time \(t\). Each matrix determines the coefficients of the system and influences the behavior of the solution.
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