Solve the Initial Value Problem (IVP):\[\frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x}, \quad \mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix}\]Find $\mathbf{x}(t) = \begin{bmatrix} \square \\ \square \end{bmatrix}$.

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Answered: Solve the IVP dx dt x(t) = -12 0] 1]*…

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

Solve the Initial Value Problem (IVP):

\[
\frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x}, \quad \mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix}
\]

Find $\mathbf{x}(t) = \begin{bmatrix} \square \\ \square \end{bmatrix}$.

Expert Solution

Step 1: Introduction of the given problem

$fraction numerator d x over denominator d t end fraction equals open square brackets table row cell negative 12 end cell 0 row cell negative 24 end cell 0 end table close square brackets x x open parentheses 0 close parentheses equals open square brackets table row cell negative 1 end cell row cell negative 18 end cell end table close square brackets$