Question

"Use la place transform to solve Y"-5y'-by = U (+-1) given IVP Y(0)=0 Y'(O) = 1

Answer 1

y s4 -by - ult-1 you-o, y 100= Apply captace on both sidos L194 sy'-by g = (ult-11) sys- syloi - y'to) - 51 syls - 403) - byls): e syess-sylos - y'to, ssylsi +5910) -byes) conditions Appty initial 4100 y los s'yis)- 510) - I ssyt 3 + 5 yule - 6yis) = yus [ 52-55-6] - ES yisi [ $255-67 - Sti Y(s) = est S(52-55-6) Apply inverse tapiaco sisk-55-679 -Sts . s(5²-55-6 S(8²-5546) ssss -6) Sub + fest

ssos if i ffistle = f(t) then zor es FISI S (5²-56-6] I f e as fisil = (t al(t-a) , a=1 S152_566) If stress-b)} Apply partial fractions - - SIS+1765-6) SLO²-55-6) SCSt66-6) - Got41) (4-6) & ans(5-6) + A2 S15+1) for poot - - for root for shoot ao - - - a = 1 & a2 = 1 took todo - 15 & 1ste) + 42 (5-6) str ess.oslo - 1 s 1 s + es Festest Ind 4 215-6)} .

14** ***** T = 116-1) (7 + 2 e (t-1) + 1 1 2 0 0 Apply partial fractions Sb 5² 55.6 [stills 6) (studis-6) 1 = R0 (5-6) + QxfS+) for noot - I no = - - / 4 ff yoot 6 ) a = - 4 Test istus Id 1 tb - i'd testin} -1967 televiden)