Suppose = This system of linear differential equations can be put in the form ' P(t) g(t) = help (formulas) help (matrices) F x₁ = t³x₁ + 4x₂ + sec(t), x2 = sin(t)x₁ + tx2 - 2. P(t)e + g(t). Determine P(t) and g(t). help (formulas) help (matrices)
Suppose = This system of linear differential equations can be put in the form ' P(t) g(t) = help (formulas) help (matrices) F x₁ = t³x₁ + 4x₂ + sec(t), x2 = sin(t)x₁ + tx2 - 2. P(t)e + g(t). Determine P(t) and g(t). help (formulas) help (matrices)
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
8. Ordinary
![Suppose
\( x_1' = t^5 x_1 + 4x_2 + \sec(t), \)
\( x_2' = \sin(t) x_1 + tx_2 - 2. \)
This system of linear differential equations can be put in the form \( \vec{x}' = P(t) \vec{x} + \vec{g}(t) \). Determine \( P(t) \) and \( \vec{g}(t) \).
\( P(t) = \begin{bmatrix} \, \, \, \, & \, \, \, \, \end{bmatrix} \)
\[ \qquad \quad \begin{bmatrix} \, \, \, \, & \, \, \, \, \end{bmatrix} \]
\[ \vec{g}(t) = \begin{bmatrix} \, \, \, \, \\ \, \, \, \, \end{bmatrix} \]
Help (formulas)
Help (matrices)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F57b95d86-4fdc-4ece-b862-dc3f5fb10788%2Fui50hzb_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose
\( x_1' = t^5 x_1 + 4x_2 + \sec(t), \)
\( x_2' = \sin(t) x_1 + tx_2 - 2. \)
This system of linear differential equations can be put in the form \( \vec{x}' = P(t) \vec{x} + \vec{g}(t) \). Determine \( P(t) \) and \( \vec{g}(t) \).
\( P(t) = \begin{bmatrix} \, \, \, \, & \, \, \, \, \end{bmatrix} \)
\[ \qquad \quad \begin{bmatrix} \, \, \, \, & \, \, \, \, \end{bmatrix} \]
\[ \vec{g}(t) = \begin{bmatrix} \, \, \, \, \\ \, \, \, \, \end{bmatrix} \]
Help (formulas)
Help (matrices)
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