Suppose 3/₁ Y/2 = = This system of linear differential equations can be put in the form y' = P(t)y + g(t). Determine P(t) and g(t). P(t) = t³y₁ + 5y2 + sec(t), sin(t) yı + ty2 - 2. g(t) = 18
Suppose 3/₁ Y/2 = = This system of linear differential equations can be put in the form y' = P(t)y + g(t). Determine P(t) and g(t). P(t) = t³y₁ + 5y2 + sec(t), sin(t) yı + ty2 - 2. g(t) = 18
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Suppose
\[
y_1' = t^3 y_1 + 5y_2 + \sec(t),
\]
\[
y_2' = \sin(t) y_1 + ty_2 - 2.
\]
This system of linear differential equations can be put in the form \(\mathbf{y}' = P(t)\mathbf{y} + \mathbf{g}(t)\). Determine \(P(t)\) and \(\mathbf{g}(t)\).
\[
P(t) = \begin{bmatrix} \phantom{a\;} & \phantom{b\;} \\ \phantom{c\;} & \phantom{d\;} \end{bmatrix}
\]
\[
\mathbf{g}(t) = \begin{bmatrix} \phantom{e\;} \\ \phantom{f\;} \end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6890296c-2fc0-4a83-b66a-ee1a85d807a1%2Fccf2c71b-ae09-4ec6-a385-67b6394fd38f%2F0edmpxib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose
\[
y_1' = t^3 y_1 + 5y_2 + \sec(t),
\]
\[
y_2' = \sin(t) y_1 + ty_2 - 2.
\]
This system of linear differential equations can be put in the form \(\mathbf{y}' = P(t)\mathbf{y} + \mathbf{g}(t)\). Determine \(P(t)\) and \(\mathbf{g}(t)\).
\[
P(t) = \begin{bmatrix} \phantom{a\;} & \phantom{b\;} \\ \phantom{c\;} & \phantom{d\;} \end{bmatrix}
\]
\[
\mathbf{g}(t) = \begin{bmatrix} \phantom{e\;} \\ \phantom{f\;} \end{bmatrix}
\]
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