Problem 7.6: Find the GS of X' (t) = 4 (t) = ( ² _ _^ ^ ) x ( t ) + ( ¹ ) e¯² + ( 9 ) t e-t
Problem 7.6: Find the GS of X' (t) = 4 (t) = ( ² _ _^ ^ ) x ( t ) + ( ¹ ) e¯² + ( 9 ) t e-t
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 7.6:** Find the GS of
\[ X'(t) = \begin{pmatrix} 2 & 4 \\ 1 & -1 \end{pmatrix} X(t) + \begin{pmatrix} 1 \\ 0 \end{pmatrix} e^{-t} + \begin{pmatrix} 0 \\ 1 \end{pmatrix} t \]
This problem involves solving a system of linear differential equations with non-homogeneous terms. The equation is given in matrix form where \( X(t) \) is a vector function, and involves exponential and linear functions in the non-homogeneous components.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2Ff9c61d49-242e-417a-937e-d18db34acf55%2Fi8dc2ds_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7.6:** Find the GS of
\[ X'(t) = \begin{pmatrix} 2 & 4 \\ 1 & -1 \end{pmatrix} X(t) + \begin{pmatrix} 1 \\ 0 \end{pmatrix} e^{-t} + \begin{pmatrix} 0 \\ 1 \end{pmatrix} t \]
This problem involves solving a system of linear differential equations with non-homogeneous terms. The equation is given in matrix form where \( X(t) \) is a vector function, and involves exponential and linear functions in the non-homogeneous components.
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