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Let k be a positive integer and y be a column vector of functions with length 2k. We have the system of differential equations y' = My, = where Mi,k+iMk+i,i = i for 1

Let k be a positive integer and y be a column vector of functions with length 2k. We have the system of differential equations y' = My, = where Mi,k+iMk+i,i = i for 1

Advanced Engineering Mathematics
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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Let k be a positive integer and y be a column vector of functions with length 2k. We have the system of differential equations y' = My, = where Mi,k+iMk+i,i = i for 1<i <k (all other entries of M are 0). What is the solution to this system of differential equations? Oh, no! It looks like you were using the wrong matrix. We still have the same system of differential equations y' = My, but this time, we have Mik+i Mk+i,i = 1 for 1≤i≤k (all other entries are still 0). What is the new solution to this system of differential equations?
Transcribed Image Text:Let k be a positive integer and y be a column vector of functions with length 2k. We have the system of differential equations y' = My, = where Mi,k+iMk+i,i = i for 1<i <k (all other entries of M are 0). What is the solution to this system of differential equations? Oh, no! It looks like you were using the wrong matrix. We still have the same system of differential equations y' = My, but this time, we have Mik+i Mk+i,i = 1 for 1≤i≤k (all other entries are still 0). What is the new solution to this system of differential equations?
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