EXAM2_M427K_FALL 2005_BECKNER

EXAM2_M427K_FALL 2005_BECKNER - Math 427K—C — Exam 2...

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Unformatted text preview: Math 427K—C — Exam 2 “ Show all work. 1. (25 pts) Solve the differential equation 3;” + 2y' + y : at + 4 — sint, y(0) = 0, y'(0) : 0 Why does the zero initial data not give the solution y = 0? 2. (30 pts) Solve the differential equation using-the Laplace transform 3;” + 2y’ + 23; = 5”, y(0) = 0, y’(0) — 2 How does the solution behave as t —> +00? 3. (30 pts) Find the solution to the diflerential equation A 1 2 —- -' 1 X’ = (2 _2)X, X((]) = (_1). Make a sketch of the solution curves for 33(t) and ya). 4. (15 points) Describe with as much detail as possible the phase—plane plot, and locate the initial data a: = 1, y = —1. | 2 1" 5341 D0 3. sinat ‘sziiaz. s>0 S 4. cosat 32+a1. S>0 5. ea" 1 a 3>“ s—a at ‘ _“3_._ s>a 6. e ‘smbt (s_a)2+b2- 5—0 7. efl’cosbt- (S_a)2+bz, 53'0 r n! 8‘ {new s>a (s _ a)u+l ’ H’fl/ EYW’hfll 0' %:«\ Xi‘- + + T w + T «I Iota/as [- Y“+Z\" +5”: 6+” +‘-|-su+t - 7(0) :0 Y‘CC‘D =0 . Ma‘th (f [gmkcrfctrmmcd COEFFICE‘VWE Ward mar. ea} +9 {and homo. eq. flaw-1:0 wt ' ' _ (r+l)(r1~I)-—o Y“ = 6 (Ct’r‘tCZ) / .. _ -1 .1; .- . .- '1 "' 016 + TF3? ’% QFIM garhcular solufions Pie _‘ For H ‘ ' . For Snot v YE! "' Hit HERA WP?) z Aug-t; 4551541; ’9‘ z “2 war, w; VP: : m: y’éz :0 ' ‘ 1972 :tAcoSt ’Bv gm‘L RH 2Ac*+ Mimi OHM-A :14 4$M=W+W-’2P6ln't 4‘9W5J‘7W+ 9 We“? Pr=‘—} * ,3?) o=x-25-e‘ MA =4 V Pr o: 6 _ \ ~ ’3‘ ' Ti- 1 W92: L! I ' _ . : ix 05+. \IPI' fiat - . (+2 CZ"? /\ q : CM») O‘W.W 25m) wind cbz+a- (505:; r‘o-fg‘xc E M "5 4m goltghofl 5:0 beams: D L "3 —\-\n.a- gyfbflflfl'l’la\ mnflo+ ‘05- " tifl%)*#+czi (1)th -2. Ejll_,_23j)+zfl=WC:t 50—5 . r 0" _ _ Lj‘(o):7_ l a 5M, {:22 52 We} ~52<i Moi-’(‘V‘CA ‘_ - .70 z (O§I-\"L03 +25 We) f—zfl» flm) : 5+: +z/ - SfiSfl 2 s +zs+\ +1-‘l ‘5. (2:22p I my: (.3, ‘ 1—? {D Fina eigenvalue. _ 2’12 ' d£+(P§—-MU=O- (1&0? 42—2)“? '1 +12 1 - _ ‘ — + +, (1—?)(v2-AF H: O 2 q 53401-4220 ' P (Mam-2) :0 eigmvames A, 2—5 7x2 : 7. 59 Find Bingc’cW H) THE graph 15 a #519le ' éourccz“ graph." Wfi \cmow +m5 bt'cause _+hr:_ 9%?) fl (Edging-$65 01* +ch: origin and gprCzIS'GQ+-_ We also know +h€9mph ls or +‘un Chen 0? wsmc car schbcECamc: \+_\S a spiral. A5 t 9a:- 5- x —)oc'> and 890C). ' The mtafl$.+ha+ 4+6, 99rd} 80:3 cub p6 ta—ooij 90 and y—Jkd LAX/h: mam), . r09) - - ‘ Tms means +Y10L+Valganvaiua m+m {qwmon ls mums-mm humW.‘ ' Splfld (Bu-H ...
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This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas at Austin.

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EXAM2_M427K_FALL 2005_BECKNER - Math 427K—C — Exam 2...

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