Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.3 Terminology for Systems of Linear Equations - Problems - Page 145: 20

Answer

$\begin{bmatrix} x_1'\\ x_2' \end{bmatrix}=\begin{bmatrix} 0 & -\sin t & 1\\ -e^t & 0 & t^2 \\ -t & t^2 & 0 \end{bmatrix}.\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}+\begin{bmatrix} t\\ t^3\\ 1 \end{bmatrix}$

Work Step by Step

The vector formulation for the given system of differential equations is: $\begin{bmatrix} x_1'\\ x_2' \end{bmatrix}=\begin{bmatrix} 0 & -\sin t & 1\\ -e^t & 0 & t^2 \\ -t & t^2 & 0 \end{bmatrix}.\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}+\begin{bmatrix} t\\ t^3\\ 1 \end{bmatrix}$
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