(b) Solve 2 -1 х. 9. 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(b) Solve

\[ \mathbf{x}' = \begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix} \mathbf{x}. \]

In this problem, we are given a system of linear differential equations represented in matrix form. The vector \(\mathbf{x}\) is a function of time, and the prime symbol (\('\)) denotes the derivative with respect to time. The matrix \(\begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix}\) is the coefficient matrix, and it determines how each component of \(\mathbf{x}\) changes over time. The task is to solve for \(\mathbf{x}\) as a function of time.
Transcribed Image Text:(b) Solve \[ \mathbf{x}' = \begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix} \mathbf{x}. \] In this problem, we are given a system of linear differential equations represented in matrix form. The vector \(\mathbf{x}\) is a function of time, and the prime symbol (\('\)) denotes the derivative with respect to time. The matrix \(\begin{bmatrix} 2 & -1 \\ 9 & 2 \end{bmatrix}\) is the coefficient matrix, and it determines how each component of \(\mathbf{x}\) changes over time. The task is to solve for \(\mathbf{x}\) as a function of time.
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