second-exam - fifi 56 Math 3041.2 Test 2 M— Do any...

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Unformatted text preview: fifi» 56 Math 3041.2 @ Test 2 April 14, 2008 M— Do any five of the following six problems. Show all work. Credit will be given only on the basis of work shown. pl. Find the solution of the initial-value problem y” — 6 y’ + 5 y = 0; y(0) = —l, y’(0) = 0. . r ,- X rz-Gr“ “'3 ULCIQ\YLC7€ 'Ic C,*C1 {‘504 :3 - r < > 3 - Jr;5'(’,c"‘t (me O: ;CI*C‘L FT (>I C7 '§(' "l :C‘-§C, ‘ VX g 1 " r .7 e v ~ ‘ft. 3» w (.— l c , '5- ‘1 7 “t 2 Given that that the functions yl = x, y2 = x are solutions of the homogeneous equation xzy” —2xy’+2y = 0, x > 0 , (a) show that yl and y2 generate all possible solutions, (b) use them to find a particular solution of x2y" — 2xy’ + 2y = x2 , x > 0. \ 7:17.430 WX$ Math 3041.2, Spring 2008 Test 2 W3. Math 3041. 2, Spring 2008 A 32 lb weight is attached to a spring having a spring constant of 16 lb/fi. The weight is set in motion by stretching it 3 in downward beyond its equilibrium position and releasing it. Determine the position x(t) of the mass at time t if there is no damping, and an external force F (t) = Zeost lb acts on the system. \/\/:Wé L: “a 160),: 71/~ 170): O "1" ‘ M : ‘ C LO 3? ~—-—~ 7c" ‘ lb‘x _ Rat/M» Uh (remtré * (-1 daw‘d— (2—! {bag 1:!" Adair! “'5 (1663,“‘4 1 , N A r’ r“ ‘ I/f - - :1" A + .h— L 72.5 r if r ‘5‘ ' J"- ' CA3 . b] , (i ‘1) e.’ ‘, t‘ , - 40.20% + [6/1604 '- Jcoa+ ‘, Ja- ‘LI (,4me [MIMI-(f . “q ’6‘)" 9 0 = HQ ISA: l C, no A — ‘ If, ..———-—-———-—-—w-——-v-~—«-—._._____._~__..——.._m..... ’5 j (J; ,1. . 'Z . ,' 35) 60 Oofl‘H FM; / henries, and 12 volts applied voltage. Assuming initial conditions Q(O) = 20 coulombs, [(0) =15 amperes, find Q(t) and [(0. @CD): 10 ., .- ‘a '- , LN? ~ 4'00 [000 2,? /—.‘H a) )H G“ Wu” AW 3 Eli}: c;e’“& are“ 3 "5' I' + I ’ ’ I .- ' '.. r for 7} in) c‘h: _$('E lez‘e.5 ‘gCL'ie—J’ Q-k SECf‘ElBr‘T‘. 1 ("lg DR ’2’0 — CI '1 ') 20v;— ._ C! 4+ 43/ I S Q,“ J cute W7 A l 7 (I Q ‘— A" , ‘\ P‘- 'P (j ' ‘2 v" IS (;('I ((I, 0) N A n “it t / , a; ,5 01?“ 5; w w /§:'s(¥f§7)+cz 3’ 1447K -. ~ /§‘ l l . Z , 1? 5 3x— ' "53’ Test 2 a? 5. Given 2x + y, y(0) = 0, apply Picard’s method to find y4(x) and yn(x) . What is lim y,,(x)? mam 30(1):Q. Wad-f 2+ an #1,. z 1 X J h in O (3 l 1 1* 1 ‘ 3 311 -— 02H? ow“; 3+J . ix 0 D (H\ “A 2 f '1 f 2‘ _f+.§l i {V ‘3‘ 0‘" 9*“ ‘-§{ eh "1 "5 473 w V” A ‘ f a. g 1 f_ "' f I 1! Mi-“ 2.. LL.“ h—vl ,x*-z‘”1 HOLE-- a“ " '3’“ #34 cu 7‘ ’5 H» “I 5'91.- 0 1 "’3 \L 3— -‘<.L "2 ‘1'!- i_ 7‘7 ‘ 3H ‘7: l 5: 3 "17?) h: EVA“ -- 1+4 ’ )0 (314.4" I Lil-I L “(I 2 , 7 3 3 21%, Li CD I 1 n _ n a .- K) 6. Fmd the power serles solutlon y— Zoanx for the 1n1t1al value problem M: can dy go: F3 7‘ {r C. _ LA" —-—y=x, y(0)’3-0. j; that“ J- ; mum dx 14:3 rhl ARV—1 new a a Z “on 1W! "‘3 6.1“ E. x “if pv-O I m w I 2 HQ» Lu; -- 2 av»: 1” l “ I H ' V2”; r an M I a Z a ZCMMQHM :1 win“ ,° 0 7‘ In] J: q' 3‘9 T 7 F I 0 _ f 1 C < L l : I1 - -7 1 qt dab ‘ (afpafi .2: *4) (:10 Ian—.l/I fl ; i W3 4*‘0'0 .Qag—ci,:( P123 43* ('71 f-'_fi t1 Chi-O « Q|\_l T__ O 3 3.2 2: 526?; ,r ' “:1: QH_ 0% 1 f 2., WI a,“ awn-L ‘r an #1 ' In ""3 “W‘- 2_ “L , .——— g (93?- j..\ I I? E 3, K I Math 3041.2. Spring 2008 Test; i ' ‘2‘? 3(1):” 3.7.1 {4 L 2‘" LO ’ '{zl‘tn MM» “(2): 63 v’ [-x ( ...
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