Question

Solve the IVP using laplace transformation

y”+3y=(t-2)u(t-1)

y(0)=-1

y’(0)=2

Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1

Answer 1

Gt-2)Mt-) dy )ult-1) -i)ult-1) (t -1) Takin hapla tnm fom on Loth Sidn (e 2 +3 (nhTt [,R-(0Rs -nhs Criv en 3Yes) 5-2 s+3) YI) 42 Se-s + 25 e - Yu) . S 223) Yu) = 2 Sts43) S24 3 S2t 3 s2(s+3) tsang fom InVLe TuKing 3-11 31 e SC&43) S&13) + 2 F1 At B tCs+D 2 S2H3 +B t est D S2 52t3 s (s'43) As Cs4)B Cs) + (cstD) s Caeftiient s3 Compay

A tC D tonparing B tD Compasiag 17 A-OHne Connpaoring calf conatant 3 B-3 D--3--2 +13 -152 17 S2t3 323) 2 2C0243) S2 t-1)uct-) - ISin (4(t-1)) ut- 3 AI t BIS+C S(s) 32 +3 1- AIls23) t(Bst C)s Lompasig laeft 4 s

ompaiy loffiet 4 onstt 1-3 AI AIEI3 .BIE-13 h SLst3) Coss CE-I)utt-1)| ut-1)- 3 Cos3 tult) Sint uE) 52+ 3) t-) ult-1) -Sin 3 (t-)ult-1) - (hh 4ct-1)-Cos (t-12 ut -12 3 Sn3t uit) Cos3t utt) +