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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
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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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?
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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