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MATH_308_A+_EXAM2_Review1_Problems_1

# MATH_308_A+_EXAM2_Review1_Problems_1 - 1.1 3 4 5 6 7 9 10...

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Unformatted text preview: 1.) .1) 3.) 4.) 5.) 6.) 7.) 9.) 10.) 11.) 19-} 13.) Useﬂmdeﬁniﬁanoflaplmelramfmmmfhﬁﬂleiaplane 2““ OSI<3 2 I23 mmthe-doumihufﬁwtapmmfmm tram-1110f f(t)={ .Makesumyuu cal-came rim-Lam am of each function. a.) ﬁt) =3 —.32! +1 1:.) f(r) = t’ez‘ c.) ft?) = 3mm 4: d.) 11:) = cos mm 2: Find up!” transform an" ms{6t) + :“+2oos(:)sin(r). Findthe Laplace Wei Ihefolloudng funcﬁons a.) f(t] :e‘z‘ +623r +5.6s —6r2 h.) f0) = sin3t—4 6052! c.) f (z) = 3tsin2t d.) f(t) 2 8—“ {50331 e.) [(1‘) = cos”! Use the properties of the Iaplace-trmform tsmmpute the Iaplhcetransforms ofﬂlefumﬁon f(r] =-tsin (2r)+ (r —1)2 +9" .Malge suréyou state the danminoftheiaplmetmmfmm. Solve the ﬁallow‘mg iniﬁal valuﬂ pmblem using Laplace transforms: y"+ 4y'+8y = 0, y(0)=1, y'(0) = -4 Solve the folkrwing inilial value problem using Laplace transfm'ms: y"+2y'+y = 9“. y(0)=1. y'(0)= —I 2y"+6y'+4_y:t, y(0]=1, y'[o)=—2 Schemefolluwing initialvalue pxublmusinglaplatn transforms: y"+9y=e“2, y(2)=1, y'(2)=—1 Salveﬁlefoﬂowingilﬁtialvaluepmblanusinglaplace harm: y"'+1.6y =0, y(1)=l, y'(l)=0 Sommmmvmepmm,. a-J y"-6y'+5y:be‘ y(93=2 y‘(0)=-1 h) y"-2y'-3y=e“ y(1)'=0 y‘(1)=—1 a.) y"+2y'+y=0, y(2)=2, y‘(2)=—3 Find the Iaplaoe transform ofthe follmingfunch‘ons: a.) e‘ sin(2t) b.) sing“) + e“: Sinai) AnimwéiMSkgisdeédm‘amg. Anemia-rm] fume F0) = 005(3)? is'apph'ed \$11199me Ellie-spring mantismmd-ﬁwdmmmtufﬁw magmas Name/m, use the 13me mﬁznd-ﬁmequam: at thematinn Ammatat-umattoﬁiemisatme equilibrium point and it is at rest. 14.) 15.) 16.) 17.) 18.) 19.) MATT-1305 Exam II Reviewlﬂ Findtheinveme Laplaceirarmfm'ms ofthe'fumtiéris': 1 a.) PCS) == 52—(521—43 1 3(5:1 —9) 35+5 52 —6s+25 5—1 (s+1)3 10 s(s+ 1)(s+.10) 334-2 52 +4s+20 332 +95 +12 ('3 +2)(s2 +Ss+11) b.) F(s)= c.) Pm= a.) F(s)= e.) HS) = E.) 17(5) = 3') 13(5): Find Ihe inverse Inplace harmful-nu a.) F(s)=£ 5 _ _ ‘ Elks—5 b.) F{8}-(5T)(s+2% . 2"”(9—2 .39) PW“.W+‘% Salve the'foliowmg initial value problem: y"+ 6y‘+9y = 0, y(0) = 2, y'(()) = .7 Solve Ilie folbwing initial value problem y"+4y'+13y : 0, y(0)=1. y'(0) = "'2 mammwmm a.) f_(t)=_=t,est<2 “TMW‘Z b.) f(t)=e‘, 05t<1 fhuperiodi c) f(f)=32'41*2) Cmpumﬂnlapmmd‘ﬂuhﬂuwﬁlgfmmﬁms a.) {0 , 0 < I < 2 , 3(1) _ r+ 1 2 < r. b.) Cl sin: “'12 d.) ...
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