Question 5 Consider the system of first order linear differential equation: x = 4x+y y = -13x - 2y where * (+/-) x = 2e ³, y ( 7 ) = - 8e ² Question 5a The system of linear differential equations can be express in a matrix equation as follows:
Question 5 Consider the system of first order linear differential equation: x = 4x+y y = -13x - 2y where * (+/-) x = 2e ³, y ( 7 ) = - 8e ² Question 5a The system of linear differential equations can be express in a matrix equation as follows:
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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Transcribed Image Text:Question 5
Consider the system of first order linear differential equation:
x' = 4x+y
y = -13x - 2y
where
x
()
where
=
(²)
2e, y
= -8e7
Question 5a
The system of linear differential equations can be express in a matrix equation as follows:
z' = Az
--^-4
A =
and
Find the eigenvalues and eigenvectors of matrix A.
-13
1
-2
Question 5b
Hence, solve the system of linear differential equations for the complete solution.
(5
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