EXAM3_M427K_FALL 2005_BECKNER

EXAM3_M427K_FALL 2005_BECKNER - t/ 01/ Math 427K-C — Exam...

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Unformatted text preview: t/ 01/ Math 427K-C — Exam 3 Show all work. 1. (30 pts) Find the first three terms in power series in powers of a: for two linearly independent solutions of the differential equation y” + 2% + 43; = 0 Find the recurrence formula for this problem. 2. (20 pts) Consider the differential equation 23323;” + 5$y'+ y = 0 Show that r 2 0 is a regular singular point. Find the indieial equation and the corre— wponding roots. What will the solution to this equation look like for values of a" near ' zero? 3. (30 pts) Find the solution to the differential equation 15’: (13):“, 55(0) = (fl), it) I (353%)- 4. (20 pts) Discuss the following graphs which show a combined plot of a solution curve and its derivative, and the resulting phase plane plot. Determine the direction of flow for the phase plane plot. Extra Credit: Solve the differential equation y” — (sinm)y’ — (cos 55):; = O I ~12o - 400.” —30 —60 —40 —20 o 20 5” +2)“; 44—h, ; WW @ Kw : a” r1 i___ a" , . .. n2 anx U " fix QM”) Km 3“; El b-ULManfl 0') r a 4 agzirI—MM an x“ 2' +2Xfifi‘an" X” + Hi0 max“ g3; _ no b0 9: 13:3 www.31me 1+ 3;, 20.. n ><r1 + 50 Haw“ P?- nil In: p‘i'Z on CD 14 D= PéolPJr'XWZMMXV + 5’33 20W” + mo (:0 m V’ a; 2010 4—3:. (H+I)(h+2)afl+lxn+|§12flnnx + LMD Jr “£3. Hal/IX a +4 3% ‘ «M j ’1 0— lab as mmmxmzmm +23% 0L» X ‘32) Yew/wane marrow. uni-2‘: ‘1ha—Y‘I'L‘a-fl __P ~2'an('n42) a» awn: dag- W20 ' Lhflflmv.) '- W'H 2. 2X 5 + =0 1 ._ l [D .‘j‘ + + 217:27 5 1 Po: £29., X1705): Mia);- g / servo Loewe ' l mu mama! ‘32:” £232) my): k3?) xfizfa): g V a WWW __ E n-Hr “9 .- ® 5— “:0 an)? 5‘: £0 ah(h+r)xm+fl “ gomthNNV-IM - 2. w — w 0'1! nianerrMn—tV-nxr‘” 1+ 5): ED anmw) x‘w'" + £0 afixv‘” - a: p 44/ 0~ viola“ (NVHMV'U'XMV + fifimimflxwm 3,, max" 0., . or ED[zan(W+V)LH+V~l)-f5anfh+i’)+ an] XHW .Wflfiéflm ‘ (2% (Va ’0 Y + ‘1‘ :D (a -»> m 2,— mmfi‘wtk “’3' 'l' 2 :0. 13+ 3r ‘>< h€ Y zero *H/Ie sMLH-wh MM \001: . WNW 'Pr‘r H‘r L9 and evwwames olenL M“ “13:0 H" ) w2. ) __ 0 (VA) (45—2) +5 2.0 (“I -§’9'7' lb -3 _) +3;\+>\ $42} -$*8=0 ‘ )‘+27\~+S=0 ',\—. *2,in ’W'ZO _._ 41:41.9 _ -2&L\Z _ -|i?;,le7,_m:i%___ 2 2 ’ 2 ' _ @HMegemem-or A: _ 11-2,: (A133) i 3’) 5 (g) tut-H20 ’2 =7 kf+qI-21fl5—f'-2)[u) L‘l -3—(—\+2' (1—21: —2>(U):(%) (Z'ZiW‘W 2’0 VHO q *ZQL w u—n w=—\ +1. BHMY l3 \Mmal‘IDL/P‘j parts, 19/”? m. * v a ' t .4 - * 4 -t - *" . &( HZL) (fig) : C tCZLtLHL) : 6 (Cogl't -\- LSMZ'EX_H¢) : _t( —cc52t——Lsmz-i: _ a _ C *Coszl: *szt +t¢oszb— Lsm'zk) ‘ t -cosyz-t- .. _t -5m‘1'l: L" 6’ (uncut-same Jr Lfi Cos'zt-smlt _.t —co52.-t __ ,gzm‘zt gm: 6‘6 (-chz-trsm'lt) + 026 t (C0524: wsm'Z'E) _. \ a O ‘ [0): (1‘ : C‘(_|>+C2( I) f3) ‘3 ) (M1 [MG/V \ =- '" Cl C" '7'" k/ t . - -sm‘} \ .. r ' " ' .. 't '45 tstE” "'1‘ Cl’H'Z E~ " " -t( “Sit-95:02.1: ’25 (“$2 2 .4 —; v [.0 ’rC/z \ Wt) C 6052 _. 3- C I t‘ '45 whit) \ “A "' ‘2— : _t cos? 2E: +6 ( .2 ‘$0521: + 15 iflw Law—v t) '5 6 Gag-t +513? . r - “MW “ “)5 21: + zgmzrt 2 ‘5“) : Cflt (,Cogz-t-fasmze \é Slt‘flyhfiad, x“ ./' UL ’G‘Yu‘gn 1 Cornea Th5 :5:th Wflfi 55¢ rm; becaua: +ha waves +0 be, QmMsmg exp 5’ch win ver’Hcmuj as) 'x Ct) and Choosing) puma an 5 U: :33 cVOnVa'ch. M60 W graph seems; +0 be 9mm an exporzanfial domxmnce “'55”? was! mm W- M5 Fumhcms dam! M3] {:70 whxm L5 Jma age-{\La’rvnd par-h 4-H: resulhnfi @haéa pmm- pla+o$ We wt can 366 +m: dommah: €>€ponen+ ‘Por whem X20 and 350.. (if )0) Jane (amen sfar‘fs mafia—m3. Tints oscillahan 50 MM 3f @ “” 5’3 +0 ! [oi-“mm wok COFYHK‘? #16:: W a... 53c“:- 80 how cubow [m +mai fflP‘anahahMér graph 1. 1 Sam \ choir)": kmw WWCM me. C. Wespo mated +0 30') by xL-t) lowi— Moe oscillahon ~HML4' hm . D6 9 GLWV‘L 4mg, mm hch. tég KHZ) blc, 6Q ='”§—:)b Jana “9mm wc Sac; m arm-Rah 2.. 9&3 .17 mm Jame, oJmev W has 6-) and G) walle WWW?) H“ W13 MNMhon w] ham 6) times. 9 WW;- ...
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EXAM3_M427K_FALL 2005_BECKNER - t/ 01/ Math 427K-C — Exam...

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