University:
Swansea University
Course:
MA-252 | Probability Theory
Academic year:

2023
Views:

452

Pages:

7
Author:

Amal J.

Q. Find the Laplace transform ofDcost - tsint4) 4te2tAns: i) Cost - tsintL (cost) - (tsint)52+12 S - L (sint)S52+1252412)S=s2+12.L (tsint) 19 = (-1) dasS2+12=sitis(2s)1.414(s2+ ,2) 2-s'+12s2Q=S2+1)592- 12siti)2 (-1)[- 25(2-11)2S=+ 2552412(2+1)22)4teat4 Let=e4 Le2tS26= = 4 1 S2SS+2er = 4 [II 4S+2)2Q.Solve y +2y'+sy - = 25t,y(o)= 2, y'lo) = - 2 L(g" (+)) +5 (CycH)= 25 ((t)=59L(gen) -syco) -y'(o).Tal SL(y(t) -y(o)] +5L (ycE))= 25x1.2= +25 +2 T2TSLCYCES+2]I= 2552L(((((+)) [sitasto525it 6 tas 2552L(Ey(1)) =25S2(s2) its? +25+5)yet) =(-125(s2) (sitasts) L(y(t)))2552(cych) 25 1 25-16Stasts 52= 25S24((C))) [if2501 25-6S2((y(t))) = 25-25-b52 3S2 (s2+2s+5)((y(t))1 - 253-6592558)S2( S2+25'55)y(t) = the - 253-654-2552 (sitasts)=2.5. 2e3 52 652+45( (+1)2 +(2)2)-258-65"+95 A= + BS+.C16 daysi(sitast5) S.2 stasts-28°-65'+25 - = (sitasts)t S(BSTC)But 5=00-0-25 = A( ++5) +0 25 QSA +5A = 25A=5equating coefficient ofS- 2 = BB==2Then Putting 1 value of A andBillin eqputting S=D-45-5(9)- -2 - 6+25 $.5 (It 2+5) t(-24c-8-22517 = 38'tc1382a= 17-38382Voglog(s + 9) 12 Hogo I log(stg)-12flogoo-leg(em=of1/1/20 log (s't4) S L log(E+1)= - 12flog[5'+4Hogle (819)