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Solve the IVP dx dt [ x(t) = 12 0 X, -24 0 x(0) = [13] 181

Solve the IVP dx dt [ x(t) = 12 0 X, -24 0 x(0) = [13] 181

Advanced Engineering Mathematics
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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**Problem Statement:** Solve the Initial Value Problem (IVP) given by the system of differential equations: \[ \frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x} \] with the initial condition: \[ \mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix} \] **Solution Form:** The solution vector \(\mathbf{x}(t)\) is expressed as: \[ \mathbf{x}(t) = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \] where the boxes represent the functions or constants that need to be determined as part of solving this system of differential equations.
Transcribed Image Text:**Problem Statement:** Solve the Initial Value Problem (IVP) given by the system of differential equations: \[ \frac{dx}{dt} = \begin{bmatrix} -12 & 0 \\ -24 & 0 \end{bmatrix} \mathbf{x} \] with the initial condition: \[ \mathbf{x}(0) = \begin{bmatrix} -1 \\ -18 \end{bmatrix} \] **Solution Form:** The solution vector \(\mathbf{x}(t)\) is expressed as: \[ \mathbf{x}(t) = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \] where the boxes represent the functions or constants that need to be determined as part of solving this system of differential equations.
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