Math 245 Ch5 TestSolns_Fall08

Math 245 Ch5 TestSolns_Fall08 - "V Prob. 4. Find the...

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Fall 2008 Prob. 1. Plot the function Math 24|5 Chapter 5 Test ( l2 November 2008) .f (t) = tu(t -l)-u(t -2) . On I ' Nsrne. Sot rrtco^ Mcs6, ?t t buc-r), 4 t u(u>=(g-t)u1t^) +u:tsit) u{:-t) I *u[b^") I -l 5s Prob. 2. Find the inverse l-aplace transform of the function F1s;: -; -l ^. ,s2 +4s+9 f* 4s+X = (s"+ 4s +a) +s = Q+z)z+ s f(t) rfi% r... s(s+z)-to =F_*Stz h*)-Q:'|-,);"5 ==@{69" F G-rr"* Gf _to O^l t $[t) = A (\fn I -lt {TI-G)I=
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Prob. 3. Find the solution of the following I't-order ODE subject to the initial condition .y(0) = 0: dv -a+bY = Ae o' + B51t -c) ' dt T.UL +f,w Lr+l^*t^dr. .p,.,^^. "+ b"+4* ;i.ij!"+ ilr3uo{n^: Jf # *bAl = {lAebt*e Er,e^o} , (s+b)Yar: * *Bdt', Ys)= Gbt F -g -"%tR, tnoenrr.,*tfa^rfr,^ , ^4 \rt)= itrYo,i = ^ii(#r.}*jl = Atdbf *B
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Unformatted text preview: "V Prob. 4. Find the Laplace transform of the function -f (t) = 4te'2' u(t - 2) . $cU - 4t zko'-*o,r-2) : qeat 'kDnL(b-z) = 4 n4 (t-1) e"*^'rr*-', + 4'Le+ -ztb^z)r1t*z) /t d'c'-)ubo,1 : a"d{d"J= S J{u.o*l =-J,f{d"l = -rt@= d:' f,{c-,>.''''1,*-a] = a"!{td't}= 6$'g FiJ,) ={tf,u}=^ ao1$.' . u uo #/ r,p i. Prob. 5. Find the inverse Laplace Transform of the function l'1^r; :;-., trs d3s xs d3J l('s)= T+3ss*2- = Cs.'-txs-l: eWA $6;O-'V'f"Vfr"J"h'^ . r \ N,S.' xs QE@D -A-S+2 r-L = Sfl A6+D +BCs+D Gol6s+r) Bc Cu.^t+oleilb' lkrurr, W- ea^^ t^f\^f, ' 1a3s Ys)=' o ' s+1.-'{ u'A t(t) =d {Vur] A+B=2 A+CB =o + 1> -28+B=Q. + B=-2 A =-28J- A= ^QB :.4-Yrsl a-rt fi,3s S+{- ' = ltcn\rr-D -2 a'ntt rruo / 6*s)s * AtlB s+2) cs+r)...
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Math 245 Ch5 TestSolns_Fall08 - "V Prob. 4. Find the...

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