iii. Does there exist a function x e X such that 50) = f + [ e*: e x(s) ds x(1) = 1² for every t e [0, 1]? Justify your answer.
iii. Does there exist a function x e X such that 50) = f + [ e*: e x(s) ds x(1) = 1² for every t e [0, 1]? Justify your answer.
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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![iii. Does there exist a function x E X such that
X(t) = t² +
e- F(s) ds
for every t e [0, 1]?
Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad4d02b6-78f1-4c0a-a713-3b04a8400050%2F54251db8-f491-43a5-878e-e38d4608ab07%2F7hy1cp_processed.png&w=3840&q=75)
Transcribed Image Text:iii. Does there exist a function x E X such that
X(t) = t² +
e- F(s) ds
for every t e [0, 1]?
Justify your answer.
![• Consider X = C[0, 1] with the norm
||x|| = max |x(t)\,
tE[0,1]
and let T : X → X be the mapping given by
(Tx)(1) = | e*x.
e-x(s) ds
for every t e [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad4d02b6-78f1-4c0a-a713-3b04a8400050%2F54251db8-f491-43a5-878e-e38d4608ab07%2Fdphph1_processed.png&w=3840&q=75)
Transcribed Image Text:• Consider X = C[0, 1] with the norm
||x|| = max |x(t)\,
tE[0,1]
and let T : X → X be the mapping given by
(Tx)(1) = | e*x.
e-x(s) ds
for every t e [0, 1].
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