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Prove L{a coskt}= -at S+a

Prove L{a coskt}= -at S+a

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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(1) can you explain in DETAIL how did you come up with this solution coz i'm going to make a script out of it
1 Ans 1:- Prove L{Et coskt}= S+a We Know that Then L ast eat coskt dt coskt st-at • coskt dt olsta)t . coskt dt -- (1) Lat --(S+a)t e - (2) I= •coskt dt -(Stajt Coskt by usng fkrmula indegadion f two functions - (sta)t Lim Coskt. e - Ceso. e (s+a}t - Jename) t SEksimet) e -(Sta) -(Stajt Lim coskt .e Ix1] Sta sinkt. esta)t dt S+a if Um ft)=0 and g) We know that is bounde d then coft -(sta)t Lim e Нете - Lim on IR. Icoskt|< | for all t eIR And coskt TS beundo d
Transcribed Image Text:1 Ans 1:- Prove L{Et coskt}= S+a We Know that Then L ast eat coskt dt coskt st-at • coskt dt olsta)t . coskt dt -- (1) Lat --(S+a)t e - (2) I= •coskt dt -(Stajt Coskt by usng fkrmula indegadion f two functions - (sta)t Lim Coskt. e - Ceso. e (s+a}t - Jename) t SEksimet) e -(Sta) -(Stajt Lim coskt .e Ix1] Sta sinkt. esta)t dt S+a if Um ft)=0 and g) We know that is bounde d then coft -(sta)t Lim e Нете - Lim on IR. Icoskt|< | for all t eIR And coskt TS beundo d
Hhen -(sta)t coskt. e Lim Then K Se :(Sta)t • Sinkt dt Sta Sta - (Sta)t .e (스Sinkt) (Sta)E {(ankt, ) I= K S+a Sta - (sta) Sinkt. ē(sta)t s'no. e - Sta Sta Sta K. coskt . -(stA) FP K K (Sta)t e Ceset dt Sta using (3) Since, Sinkt rs also bounded on IR |Sinktl $1 fer all &EIR - I= Sta (s+a)2- I = S+a > I (1+ ) * a S+a (S+a)2 Sta (s+4)2 -) I = (S+a) 6+a) From 1) and (2), we get Lf ent cosikt} = S+a Hence proves (S+a)? + 1e2
Transcribed Image Text:Hhen -(sta)t coskt. e Lim Then K Se :(Sta)t • Sinkt dt Sta Sta - (Sta)t .e (스Sinkt) (Sta)E {(ankt, ) I= K S+a Sta - (sta) Sinkt. ē(sta)t s'no. e - Sta Sta Sta K. coskt . -(stA) FP K K (Sta)t e Ceset dt Sta using (3) Since, Sinkt rs also bounded on IR |Sinktl $1 fer all &EIR - I= Sta (s+a)2- I = S+a > I (1+ ) * a S+a (S+a)2 Sta (s+4)2 -) I = (S+a) 6+a) From 1) and (2), we get Lf ent cosikt} = S+a Hence proves (S+a)? + 1e2
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