Test 1 - \. WWI} l iii/"A . ‘ ‘l ‘ k i F“...

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Unformatted text preview: \. WWI} l iii/"A . ‘ ‘l ‘ k i F“ Test 1., 427K, 19/ 01 / 2009 _ . ' u- kmé‘fiRINTED NAMEW Every problem is worth an equal number qf'iooz'nts for a total of 100 points. i ‘ You must show your work; answers without substantiation do not count. Answers must appear in the boa previded! (I) Find the solution to the Initial Value Problem ty’ + 2y m sint/t ; y(—7r/2) :— 4. V‘ “i7 {2“ w: :1 53"” ) ‘5: '.:2 ,= (I. '5 2 J \t a .r i , - a; " e,- . 2 Z a ‘ \ if“ ? QM 5t *2 LNL in“; lggl’l: “5LW‘5'0 e1,” ac: . , E; f L '2 E w gig/“AIM k L \A} .w i v"; (“’1‘ xii-Kl ’ E "2 ll, 0} M ““ (/03 if L) j“ \— L ff M Lj : m K L) "A" Fri—W (4;) n he I: Z : é 9" C _ . Li L ; Lil A O T 171 L: W L‘} —. 'L hm. .5.‘ ~— *\ Answer: y(t) :2 W‘>{ xx) H) A tank originally contains 240 gal of water with 90 lb of salt in solution. Water containing 1/ 4 lb of salt per gallon is entering the tank at the rate of 2 galllons per minute. The mixture is allowed to leave the tank at the same rate. Find the amount A(t) of salt in the tank at any time t. \[0 I; f; {:0 3") {'f'm'K? QM {51.35 ,a:-. w ‘95,. Q; (it? '5 a a Q [ lb {‘3 1 "5 Aw» “E333 if); x '2 U HI 0 “l (75\\ Mr " W (a /I /\ cm~[i)(f/ to \ t H or I69 .{x l E ”‘ g t: I} I 'U ‘3' e3 * b . 1 . (,1 1/”: {Q ,. C ’ £0 3 - 7 (111) Find an integrating factor ,u .F' f \ i 3 Mg fl MK M m « My W n I‘m. a”? M MA a -— z Answer: ,u ‘5‘ a7lvey diff—14 (2:1: — fley)=\;dy : 0. a’in- L)?— a”) + K 6‘4 a" . w (IV) Solve the initial “3,131”?w ‘gifghiem 2y” + Zy’ + 2.5g 2 §4_lsin~t~~;-my(0) n —-16 , y’ (0) m 1. f_,_.»-...,.—..w- T +4 rs . ‘ 1 J , h 0“ ““' a ‘T‘ EU mg, r—wmw.m‘mmwmmumm 7‘ Kj I mm V) State the existence and uniqueness theorem for the linear second order ordinary initial value I problem. [Make a. drawing if it helps.] ' ‘ - ‘ .. 1' - A n , muffi‘hq? U WA Sufi y. m .3 m} . 9 3 03 owkél 0M; 0M {0 62(0wa ) jg )7; 67? n a _ {:3 I W*%““§“"y"w3 Wfi 0n Como W Miaman (R j I U? ‘1 W Lewya,§ivzg__flh m w W. ‘ I I] g - -- {:fi“‘---§"~Wf‘~ t d é ” x J; é’fiwgfik JLJK Var-,WS “g f; h, (Ufl { 4/ fl \l u u §€?{_{a.)€{ 0“ \ ~ ...
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This note was uploaded on 03/24/2010 for the course M 56930 taught by Professor Bischler during the Spring '09 term at University of Texas at Austin.

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Test 1 - \. WWI} l iii/"A . ‘ ‘l ‘ k i F“...

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