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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 41CR
Related questions
Question
Given initial value problem:
y' = y/(xln(x)), y(e) = 1
Transcribed Image Text:d) Suppose the rectangular space D around the initial condition has a width 2A along the x coordinate and height 2B along the y coordinate. To
satisfy the Picard-Lindelöf theorem, we need to fulfil conditions that
Ol and II
OI,Il and III
Oll and III
I:y/(x In a) is continuous and bounded in D;
Hy/(x In z))
II:
ду
is bounded in D:
III:A <= B/M, where M is the maximum value of the absolute value of y/(x ln x) in D;
e) Thus, in order to guarantee the existence and uniqueness of the solution to the IVP, A and B need to satisfy
Ol and II
Ol
Oll and III
Oll and IV
OIV
OV
OIV and V
I:0 < A< eII:A <
III:0 < B< (x – A) In(x + A) IV:0 < A< e – 1 V: B, >
(B+e) In(e+A)
1+B
(е-А) In(e-A)
Transcribed Image Text:y' = y/(x ln x), y(e) = 1
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