EXAM2_M427K_FALL 2005_BECKNER

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

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online