-2 3 ㄴ X " dx ㅜ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve the system of Differential Equations with the given initial condition.
![The image contains mathematical expressions involving differential equations and matrices, suitable for an educational website:
1. **Initial Condition:**
\[
X(0) = X_0
\]
This represents the initial state of the system at time \( t = 0 \).
2. **Matrix Differential Equation:**
\[
\frac{dX}{dt} = \begin{bmatrix} 3 & -2 \\ 1 & -1 \end{bmatrix} X
\]
- This is a first-order linear differential equation involving a matrix multiplication.
- The matrix \(\begin{bmatrix} 3 & -2 \\ 1 & -1 \end{bmatrix}\) is a 2x2 matrix.
- \(X\) is typically a vector.
This system is used to study the behavior of dynamic systems where the rate of change of a state vector \(X\) is determined by linear transformations represented by the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d0ee2cb-cfe2-4eb9-a097-d38324436758%2F5c4f9e18-480a-4a78-94b7-e2dcdd2bc546%2F25ueooj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains mathematical expressions involving differential equations and matrices, suitable for an educational website:
1. **Initial Condition:**
\[
X(0) = X_0
\]
This represents the initial state of the system at time \( t = 0 \).
2. **Matrix Differential Equation:**
\[
\frac{dX}{dt} = \begin{bmatrix} 3 & -2 \\ 1 & -1 \end{bmatrix} X
\]
- This is a first-order linear differential equation involving a matrix multiplication.
- The matrix \(\begin{bmatrix} 3 & -2 \\ 1 & -1 \end{bmatrix}\) is a 2x2 matrix.
- \(X\) is typically a vector.
This system is used to study the behavior of dynamic systems where the rate of change of a state vector \(X\) is determined by linear transformations represented by the matrix.
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