MTH 205-Solutions of Final Exam -Summer 2007

MTH 205-Solutions of Final Exam -Summer 2007 - College of...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: College of Arts and Sciences Final Exam — summer 2007 Differential Equations (MTH 205) Instructor’s Name: El 1. Sadek El 8. Khoury Date: July 25, 2007 Student Name: Q ;> Student Number: ———______________ Section'Time: This examination has 10 pages (including a blank paperfbr calculations) plus this cover page. Before you start the examination please verify the number of pages. No Questions are allowed during the examination Student signature: 1. {12 points) Use Laplace transform to solve the! following systmn of dif~ ferential equations: (17.1: *— : —' .~— ‘2 (if. 9+ 6“ ) (fly —~'~ = 4' (it 1 + "U such that ;c(0) = U and MO) = U. 0 .15 0 “(Hr/2%; =3><w> +“‘<~s> -15 SXIS) “‘4' Km) :: e "3 X8) +5305) flung!» :o XIS) .fi. K‘s) : -—l}\ +>E1XI5>+ (gm/1‘05, ta \ \(Ls) -: 36 fr! 5": 1 *2; + 1: 5-") X19 1‘36 i '25 :L-- “r f 5"! 5“; j J g” -' é ’1 { § $a("c\:§[‘£ 7:? +36 523 £- .— .-— 3 )Us‘) 4-8—1)ng :3 =5; 5 «‘45‘H’ X“) q-fl‘: 33» C? 5' '15") 2 2. (1:3 points) Find each Lapiace Twansjbrm. (i) £[tsi115t] L. _ EL 9' 3 ___ g ('15) __ 1a:- cJS 5"+L5 3 :31 I“ ) 7’{/+;:t2_.{’ur4=-\) +3Ui ‘ S J ‘ 3g; 1 be“)? T . o/{fhlg ": E—g‘ ~— S '2; 3e 1 ,5‘ {tz+;t1—\§ + I. 5 :5,— t L 36 6,} ifzg-Z'f Ik’f‘ _——-—j .— .2“: ---- 5-3 #5 #1. f '5’ 5 +3.3!— 96’5 743—“ “'3'— S jag-'3 —-" 7:.- J —S if“) S '5 23—— + T ‘2‘” J 5” ,. 9.. I} 164(54 +5"; 5) ~._ 7. ,_ (in) u—lw *' 7; x -y 3 - I ~ ‘— 25—‘43: __fl ’- J “If 1“ “b’z’ L5H) 5’59 if t‘é“..z£ é +5 (9—H) 3. (15 points) Find each inverse Lupiacc Tmmflnm. (ac—1W]: {'i 534—5 5 rib—H} :14“; * fulfil .3 [9‘75/«679nék4 — J’mfclz: k:( 0 film—E [-65.9 ‘ "“bfL (ii) 51%] 2., jfllffim —! 9,5 = of f -1 25+G’é :/ -1 J #éz" 5; f :M fw m ri‘éjfws'f _éé3£fin 5'15 4. (10 points) Solve the following differential equation. Give the solution in explicit form. .r y’ + (J3 + 1) y z 9"" 111;:- .4: r. __ C fix ...__’vi__3’-_-_ D +Q+15‘)3 " x w x6:— j{l+ik)ék x443”: 1 f4”) : C 1-: 5 :16 ‘éll) I Ddij'efx' Ak— 5. {H} points) Find the general solution of the following differential equa- tion [Use the undetermined coefficients method to determine the particular solution). If!!! + y” = 1-— .. Mg—tw’" =0 ‘9‘!“ (WH\"‘-’ :53 w:c, Qéa‘bkc> ) “.24 lbs/ll :: C‘+<-2.’C +3ewx- p]; $3.? :? 76.2217 ‘1 } HDF: {761i}, 9C1} 6. (10 Points) Find the general solution for each of the following homoge— neous differential equations. a. .123 y'” + ary’ = 0. b- y” - 8y = 0. 6 m(m-—I)(w-2\ +h=0 m(h1_3m+18+m =0 m (“1-5M +3) =0 2::J9—fi. _£-;El‘ '3. “:0 m = ‘ I 'l- C“ 3/ m1 1' (ficmofiLQ-f CLSIh {gill “4:1 W1+1“.+Lr:o vim-:1) w:,1_‘F- NIH-'4‘ 7. -— Hi 93— alt-F I'm”... -"+ .pL) W ._ _______.._..—::—— .—- 7. (12 points) a. Use Laplace transform to solve the following integral Equation: 1 I »r If“) 2 if?! — it")! + I 0 (ET -— f3’-T) if“ - T) (37' '* H ‘09):J5 E's—st”) r if/(e-ge )dt‘a) '3 - I .l_ YUM-J— “ 5H + 37*5H)V‘5‘ 3'“; -X I XML-,- 2 +5“; " ‘(H IE»; 5 -| (I '- .3— (Q: 1—...— Sb")\( 5"? x 3 2(;t_1\ Sli— 3 K“) .3 2 1:) (S - (5:3)(5‘L)”+l‘ 5"! :qu 5 + c .2. z [5)- I) (A; +6)(5.t-'1) 1- ((3:0(511) 54,3 I-e 5+; +D(S‘l—3){5-L) 5“ =9 ( -..L,o =) arm Era-1 a: 6 :41) 737 “=41; (FMsM-n :5 J; *‘5 “V S=fi=§q=€rhfifflé 3-6:“! = - 1' ' “HG g) H 3 W—zé =9 358:“! Jr“ =‘1 => h:o 2.1g waft ' am =43. mm - 2;} .. ac b. Find the inverse Lapfiace Transfoma. WMSBH” 11:, ‘4 Fm} Jiifmj :- “éFM =9 1PM =3" {as u 8. [12 points) A mass weighing ‘2“ pounds stretches n .5- ;m‘ing foot. The mass is initiaity released from a point ft below the eqniiib-r‘inin position with. or, downward Unionity oféi ft/o. 5:. Find the eqnotion of motion. 13. Detefinine the period. freqnency, and omptitnde of the motion. 0. F ind the iricutimnm displacement of the 3 ping from the egnitibiinm po- .sition. d. At what. time does the mass pass thran ing downward for the second time? oh the equilibrium position head- 9. {1i} ].}oi11ts) Solve- thc :i-ifle'r-ceutmi equut‘éu-nh Grim: the sofiution m explicit .. z“ 3 ‘ 2:17'yy'=4;53+3y2 # If)” '(‘t r 3 form. =5 u’uéu = (“NH-11353" 77" MNAW r: xILLH'u“)At a. an “I :- fiAL +L u‘--H .Q Woo-H) :: thdfc (=3; u‘+"\ '5 A1 a) u“ :1 Pm " s’) u r '1 W =17 3:; = T?" \J P” fir :: '51" 3‘ J k1 rt! 395 ...
View Full Document

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.

Page1 / 11

MTH 205-Solutions of Final Exam -Summer 2007 - College of...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online