MTH 205-Solutions of Final Exam -Summer 2008

# MTH 205-Solutions of Final Exam -Summer 2008 - Department...

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Unformatted text preview: Department of Mathematics and Statistics American University of Sharjah Final Exam - Summer 2008 MTH 205 — Differential Equation Date: July 22, 2008 Time: 2:00-4:00 pm Instructor Names: Dr. I. Sadek [I Dr. M. Anabtawi El Student Name: e Student ID Number: Time of the Lecture: 1. Do not open this exam until you are told to begin. 2. No Questions are allowed during the examination. 3. This exam has 6 questions. 4. Do not separate the pages of the exam. 5. Scientiﬁc calculator are allowed but cannot be shared. Graphing Calculators are not allowed. 6. Turn of all cell phones and remove all headphones. 7. Take of your cap. 8. No communication of any kind. Student signature: l.(10 Points) Use Laplace Transform to solve the followin ential equations: 3 system of differ- 2. (12 Points) Find the given Laplace Transforms: (i) £[z7e—5e] = {Hiﬂer*r "' 51's)? where f(t)'= { 1, £22 .1- —P. J £{te‘2‘cos3art} : OSt<2 iiu‘ff‘q + £79" {th ﬂ] 3. (9 Points) Find the given inverse Laplace Transform. ‘C [32+45+13] : '3 +lfs+"-‘I‘il3 .f " ﬂ 4 5192-:- __ 51-:L ﬂﬁiY-L. S _ z (Rafa-1 E‘ f i ‘ K cm)” -2 —1. : c £60534. --.3=..9 ﬁSmS‘t (ii) -1 —2.s Si 3 ] c [8 (3+32+4) = 3 Ulk-Z) '1' WZH'I)U+{—z) i3+¢anlbﬂ “a” 7- (111) -l _, 1 | 5 [Mid .. J— 4 I 3 i islﬁ‘f {HM = i-JEka =s‘1t’L L :- surge}: o T:{ 3.60? l T3,; ': 4- - C05": 4. (12Points) Determineasuitablc for f .fth ' fgfﬂicients is used. You need not to aging)?" clam 5111;211:0121 of undetermmed 31”"?J'+%y=3+gi V. L a z ‘ x ‘3‘, m - M +12- =\'-':'1 \$ (M‘I‘V‘) :0 =9 "III/"VI \$59 I)ng '1': :6‘2. + L, a. a ’L J-x “Pl ‘3', .. A-rBf'c‘ (b) 9“) ‘y"=4m+2xe‘” M M” - m" = 0 =9 mum =0 1:; wroﬂjiﬁ -x 9 31/1” c kg} -'x+.c 9c \SC‘A) = C; -\- cw“- ‘K' 9.1" “ n ‘1 ‘3“ ‘3? - Axaa-Bx“ +C2e +Dade (C) y(4)+4yﬂ=5in22+tct+4 “A “4“ +Hm":o 3 ﬁ1(M2-\'R :0 Q m=ﬁ,¢ W: "\$9" 31,1) Smu)¢:asz{£ ‘5“) g C‘ +6.“, +C38w1£ +C‘6olt 4‘ - ' l: + treat ‘39): Ag' Jr 3&e't .‘. C e. + Sm'z. E- 5. (14 Points) Solve the following differential equations: 0) If! y +6y”+11y'+6y=0 m‘+"ﬁ1+“m+‘ :0 ma”! :9 ...|+6—Il +6 :0 (True) M 13 o m”+§ﬂ +6 (mu‘)(_m+3 “H- = w. :4)..3’..2. NH m’+6m"+ “a 1-6 .? .. -3: .111. -ﬁH-M" 1"“ 'c‘2 +61; *C3e 5’m‘ +um / 5 1;]. a. 6 o 0 (ii) maym+zy:_y=0 "“MﬂXM-IE + In --L =0 hm") ("Wm-1) + (3 = a (“’0LM1—2m +{\ :0 ’- -l (In-l) [H-13 =0 QH‘J‘AA Em - 0.76 +‘tgx(ﬂnz)+chuux)1 ﬁm = c. + cu: +c1x \$[ﬁl5=co +£‘1 +1i-cox} __|z cgsx'f*l0bm ’_' _ 12\$“... W»: com w xL-a-l-z”+.L>?"--BI+C.=74;-’~— j, '- . l ) 7. (10 Points) Use Laplace transform to solve the follipwing initial-value problem. i y”+4y=85(x—2w), “(3:31 y,q0)=0 A” ‘3‘} ‘Hig'ﬂ =' 5 ffsquml S'Km -s‘rc) “(my +H\(195 : E e '5' “3- 39:24: +I‘Sln ELK-is“); t b1“ 8. (9 Points) Solve the following integral equation: y(t) = t + foeyfrm'r + [out — 1‘)y(r)dr‘ I': ihml = + {(Ijtnét‘k .f- '13‘3‘04‘} m = J: + + 2W0} 5 5‘ 5‘3- 5z’5 " " >YG‘) '= "L" 54’ ( 5/ (5 z: a K5 51-5’L =7 3m -.- ﬂ!" { (-5 - (WYE. Va-é gm =§ge 5M» E“ 9. (12 Points) The temperature of an engine at the time it k shut off is 200°C. The surrounding air temperature is 30°C. After 10 min have elapsed, the surface temperature of the engine is 180°C. How long will it take for the surface temperature of the engine to cool to 40°C. TLO»: 1009c ) Tm: 300C J z '90.:- ﬁ'al f w‘m 77(5):.1/0": ir=kCT_Tﬂ\ % —-'—T-J'T {kale +c. at —,m I kt -=> 711’“ = Ae he QW :TQ‘V Re kt 9 We»: 3:: + he :- l?0 T(°3.m-%>Qaa :30 +P\ “'3’ A H s»qu -.: 30 4; ﬁne fol: Tannin =2; we :30 +H°e => ~*=*(:’§) e11??? ...o.\1.\$'1.L 7:; Tun: 3o air-Fine "Mud earn” ...
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## This note was uploaded on 02/12/2012 for the course MTH 205 taught by Professor Sadik during the Spring '11 term at American Dubai.

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MTH 205-Solutions of Final Exam -Summer 2008 - Department...

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