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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
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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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