call the admissible class of functions Ao = {ve C¹ [a, b] : v(a) = v(b) = 0}. suming u € Cn+¹[a, b], prove the following statement: cb dn u dxn v'(x)=\v Ao ⇒ u(x) is a polynomial of degree (at most) n.
call the admissible class of functions Ao = {ve C¹ [a, b] : v(a) = v(b) = 0}. suming u € Cn+¹[a, b], prove the following statement: cb dn u dxn v'(x)=\v Ao ⇒ u(x) is a polynomial of degree (at most) n.
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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![Recall the admissible class of functions
Assuming u € C+¹[a, b], prove the following statement:
cb
[d
a
dn u
Ao = {ve C¹ [a, b] : v(a) = v(b) = 0}.
=v²(x)=0\v € Ao ⇒ u(x) is a polynomial of degree (at most) n.
dxn](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fada21877-31ca-41ff-a148-98049a3848f0%2Fc9455354-ffdf-4c5e-8d0f-e0ca9e1946e9%2Fmz7gwcq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Recall the admissible class of functions
Assuming u € C+¹[a, b], prove the following statement:
cb
[d
a
dn u
Ao = {ve C¹ [a, b] : v(a) = v(b) = 0}.
=v²(x)=0\v € Ao ⇒ u(x) is a polynomial of degree (at most) n.
dxn
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