I have already attempted all the homework question
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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I have already attempted all the homework questions. If you could put detail into the answers as I think I have messed up somewhere but I am not sure where. Thank you.
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(a) Express the following inhomogeneous system of first-order differential
equations for x(t) and y(t) in matrix form:
i = 2x + y + 3e,
ý = 4x - y.
Write down, also in matrix form, the corresponding homogeneous
system of equations.
(b) Find the eigenvalues of the matrix of coefficients and an eigenvector
corresponding to each eigenvalue.
(c) Hence write down the complementary function for the system of
equations.
(d) Find a particular integral for the original inhomogeneous system.
(e) Hence write down the general solution of the original inhomogeneous
system.
(f) Find the particular solution of the original inhomogeneous system with
I = 3 and y = -3 whent= 0.
(g) What is the long-term behaviour of this particular solution as t becomes
large? Does the ratio y/x tend to a fixed number, and if so what
number?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0557e0e-7c52-43d2-b9f4-a887bc43498a%2F10a652a3-8b8e-471d-b85f-6a239a923b7f%2Fyllpmnmn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A - 11 - OneDrive ×
19mst224tma02-j.dvi
sonal/zx848348_ou_ac_uk/Documents/Year%2... Q
nỉ - OneDrive
OneDrive
3 / 3
103%
(a) Express the following inhomogeneous system of first-order differential
equations for x(t) and y(t) in matrix form:
i = 2x + y + 3e,
ý = 4x - y.
Write down, also in matrix form, the corresponding homogeneous
system of equations.
(b) Find the eigenvalues of the matrix of coefficients and an eigenvector
corresponding to each eigenvalue.
(c) Hence write down the complementary function for the system of
equations.
(d) Find a particular integral for the original inhomogeneous system.
(e) Hence write down the general solution of the original inhomogeneous
system.
(f) Find the particular solution of the original inhomogeneous system with
I = 3 and y = -3 whent= 0.
(g) What is the long-term behaviour of this particular solution as t becomes
large? Does the ratio y/x tend to a fixed number, and if so what
number?
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