Consicer ol diffontial eys %3D where, 2 is di fhaential oberator on finction space de fined fox bolndary foints f(0) is dde suitale x E [dob], d ohd b d Source fn ond ylo0) is or both of Jocnday pornts The im hosel at one Green fon is defìnel to be solation of eys whese oberator I es Understand to oberante only I-Cordinte, S(-) 3 dirac-delta and G(acsto satiofies some a). Show that 40) to ey@? b). How B.c's s does 4 (x), SGoot) $lt)dt s solution ote the bondazy Conditions included in. above lution of f (o0) ? :Cahich bet of above odution y (oc) Would chonze a if bolhdlary conditions imposel at a ond b chonzed e c). Now s Couseler operators I = (-1)with BC° 님 (oc)→o I 5how Gden fn fur this will bes for x>t ond verifu it tia Sree deruided Bo lhady Coredition?
Consicer ol diffontial eys %3D where, 2 is di fhaential oberator on finction space de fined fox bolndary foints f(0) is dde suitale x E [dob], d ohd b d Source fn ond ylo0) is or both of Jocnday pornts The im hosel at one Green fon is defìnel to be solation of eys whese oberator I es Understand to oberante only I-Cordinte, S(-) 3 dirac-delta and G(acsto satiofies some a). Show that 40) to ey@? b). How B.c's s does 4 (x), SGoot) $lt)dt s solution ote the bondazy Conditions included in. above lution of f (o0) ? :Cahich bet of above odution y (oc) Would chonze a if bolhdlary conditions imposel at a ond b chonzed e c). Now s Couseler operators I = (-1)with BC° 님 (oc)→o I 5how Gden fn fur this will bes for x>t ond verifu it tia Sree deruided Bo lhady Coredition?
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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Question
![Consiler d
chese, 2 is di fhential aberator on finton space
de fined fox
boladary foints »flo) is
*E [aob] d ohd b ade suitble
d 8ource fn ond y lo0)
boundery Conde tions
is
im posel at one
or both of boihdary bornts The
Green for is defined to be solation of eys
%3D
whese oberator I s Underntaed to ofperate only
I- Coordinate , f (oc-t) cs dirac-del te and G(acs to
on
satiefies scme
B.c's
s does H (0)
a). Stow that y loc) = Ī Goot) f(t)dt cs solution
to ey@?
b. How
above slution of ų (o) ? :cohich pet of above
nodution y (ox) Would chonde a if bolholery conde tions
imposed at a ond b chomzed ?
c). Nou Cosder aperaboro Î =(d - 1 with Bc°
the bolndazy Conditions cncluded in
olte
%3D
I 0.s how Gden fn fur
this will bes
for x>t
Chd versu it atia fre derliaed Bohdy Coreditieom?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66578098-c5d5-436d-b59c-5cded03aa021%2F0418e77f-a2ab-4105-9d3a-e9ec59cca392%2F0337i5y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consiler d
chese, 2 is di fhential aberator on finton space
de fined fox
boladary foints »flo) is
*E [aob] d ohd b ade suitble
d 8ource fn ond y lo0)
boundery Conde tions
is
im posel at one
or both of boihdary bornts The
Green for is defined to be solation of eys
%3D
whese oberator I s Underntaed to ofperate only
I- Coordinate , f (oc-t) cs dirac-del te and G(acs to
on
satiefies scme
B.c's
s does H (0)
a). Stow that y loc) = Ī Goot) f(t)dt cs solution
to ey@?
b. How
above slution of ų (o) ? :cohich pet of above
nodution y (ox) Would chonde a if bolholery conde tions
imposed at a ond b chomzed ?
c). Nou Cosder aperaboro Î =(d - 1 with Bc°
the bolndazy Conditions cncluded in
olte
%3D
I 0.s how Gden fn fur
this will bes
for x>t
Chd versu it atia fre derliaed Bohdy Coreditieom?
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