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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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