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SolutionPracticeFinal

SolutionPracticeFinal - Math242 — Practice Final Film...

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Unformatted text preview: Math242 — Practice Final April 22, 2010 Film] Exam: One piece of paper (1}. X 8.5) with handwriting (not photocopy) is allowed; Two more challenging 13111131631113 for 13011118 points. 1. Find the general solution of 11 ‘ ‘ ‘ :31 = 1 -+~ (1:2 + (0'2 + x2312, (1:1: fiiiEkEGfi 5% ”fo;)% fUJi’E) fika—XHifl M. mfg/magi 2. Find the particulaz Solution of 3. Find the general sohfinion 0f :r'jy’ : may — y‘B. \ , X} 3 $3th W” m ‘ «:2; ck? 4. Find the pmtimlar salution of (ET + yew + (By +s17€3my)y’ : 0., 391(0) = 2 3.3.! «39% 2': QTMWW Hack Q KW )5 fii‘fi Mi fl X _ 3533 Mé‘g 53> WW 1? 5i 3 W <~3§¥am W‘fi-Hm 2% (WW Mm; ($39ng g C; 5. Find the critical points of the given differential equation, determine Whether criticai point is stabie 01' unstaifie, and soive the differential ecgiation explicitly. (1:17 . Ezrr w5zrw+4u im im" fiM W1: xiv-MM; jiK'fifliflk)‘ D ‘ Kg’fi' Xi“:- fimmmgkfiimm .25: OT kt; fimmm k2: §K2§fifit \fsfiihim ) Fab W Wm M $0M % W) _... gw‘mm 2km) . 6. Use the RungowKutta method with step size h = 0.5 to approxhnate the solution on the filterval [(3, 1]. 59% k W? m i {a 3; 35) JYUJV k . 5W)“; H 9:73th : 3:2 +112? 5W Li . gr 5:“25 6 7. Find the general solution of 612;“) + 113;” + 4y m 0. 3% MW 2 ©ka Eta $me (4%" J: H fl Ar: 0» (2m 1} WW :0 ”333g 1 i: 駣 ,, Effliéfi 9i? 8. Find a. particular solution of 1 ML 33> Br;- 3%“) A: v” fawn ? gm? fiwwm 5K 0LT WT 5+5 9‘ (a): Find the Lawlace trausfm-m of fit) 2 (3‘2" sin 37rt; (13):?in the inversse Laplam transform of F(s )— — JUTANTW 5 5k IL U OLWWT £5,555 55555 ”3T "-55% «:2:- aim: T“ 5 CH Q m T (Sui-TATE? 55.4%,” r 5 5 ((5,339 U 5* 5T " 55555555525) 552 5‘5 (55556555) T BTSMTWVH (CSTTTSTJT 5:»: 2 :95 T36"; '57; 'l 10. U 86 the: Laplace tral'lsfoml to solve initial value problem x”+42:’+13x=te”‘; :r(())=0, g;’(0)$2. lMW*cUflm:SMWfifiwzw%> glam} m S‘MW msmwx’w) . :2 3"” X52) «:2; ,. . "l §m$a+%Mbw €&@W $7 W . l __ 915% — Wislwié‘g)’ 10 l 3; null, mm 506 albamwje'l/W w; ‘ ...
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