AK-MATH225F09-WS5

AK-MATH225F09-WS5 - MATHEEE, Fall EUDQ Name: k Worksheet 5...

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Unformatted text preview: MATHEEE, Fall EUDQ Name: k Worksheet 5 [2.1, 2.2, 2.3] Sectifln: Qt! Girls For qu credia. you must. 3110“? 3.11 work and boiranswers. 1. Consider the differential equation, which models a damped harmonic oaciflator. *‘u‘ y”+2y’+5yrfl j 7 __ __Z/l7’ (a) Show that ME] = a“ ma (3:) is a solution. yr : “5:15:55 : m HZitfiTn d 2L) + _ ,- — x ._ ‘fi: . _ H =3 E UCLfig-th + ZaETWLZi/D f2;%rniZt)“ LIL CnSfZO 7 _. _ arb- l. * h I u I r I .13déd ~} W194. .. ,. J-_2Lt.qual 2. Given 2(1— g)? my —2y + 4mg; slssle (a) is this system linear? {h} This is a [modified predstnr-prey model. Which variable represents the predator and which variable represents the prey? x ,I 7 1 f; rnajafior {e} What type of growth does the prey exhibit in the shsenee of the predator? __f________ .__ _ _ 7:01 at = a News [Lazs’clflii {d} Find all the equilibrium snlutinns [points] for this system. A): _ _ 01 jg “ lU'Eseryto ‘4‘ f3 '— ~Z)+LJX)-TO if blxb :: .. XL 2 ‘E‘ ,7) 0 7-119; LIX):C) uzb X {Z- fljzfl : f + = 74/ 3 La O 2 LEM—LC) XFG Z-QL:O KI; :1 3 11:3 X34 r _t REP ', o O 1 I Zézfié7>_—© _ M J/(E’b/Dg . J S g __. ll'i (EL/E “33’— ; lilti- E‘“ flat" X[{)=D,7[t}:Q — i tie-3,;mw 3. Given dl' gt" — —‘2$ is _ = 2 _.-""_4 [it “(x L' [all Is this system linear? :05; {In} Find the equilibrium ssiutisnfls] for this system. ifi=fimHD s4 §g=as=s>x> C‘J-X 55E: : 1" 5H : {X ‘9“ 1X )1?) J * -2:i "2‘ ' Z r; -H 53:: ‘. cl; 4211s 32* (A t 7 "L aziwédv asrxi zi—LZim m. 1 ‘1 . mt . a) _ -1 1m A = sac: “‘Wflfms. . f + 3—st ‘ ~ vi? 4 L t w; '91s; H: r r!- 71'“ L“ 39’" Wit WH- I' TAX 4 2-K I‘D / X :5: ,« X3”: F + Lita K‘s—L} M {Zr-L Ff: {Ht FL”+?s ’73 figh2J<E 4 ..‘_- D FT— ‘— I. A 1ft ._ - -} Z ‘_ XL'C) r ma} : Kc, 3*} 7*” if. H7P_tzri7s {d} Find-the partial-lfi-sslutjsn that satisfies thlIEEIislcsndition {x[fl:l1y(flj}= (13,13). 7P: {Ki rt fltgjlfls:D/£,=o who“; 75c») : M15” +0 =61 , 35C) . 06:1 t Xa'):fl $717735 7'5 {is ‘3 -— N r' K :LH? "'1‘: ZHLO Efifi'i'bflm % ‘ '_ C11. _ g ‘I: J aim” stwlg 413st; 1|. l‘ .. ....._________ Lrnaftwi h "---—..___'____-_ G- /+ I . . ____ _r:__ L"- fégqfi I ' -. . r] ~ I“ "' l..____-____“—" .._a" _____ .- "" —_________"_I_I _ . - fr: 5;} A ‘)I: 41. Given E — ace“ dy _ E dt _ ‘3 (a) Is this system Linear? M5: Cb] Find the gonorai solution to the system. PR;— QJI {LCD OP {fig/L I Wax—i- dfi’j‘: Uri”! - [M‘H- ‘fll'r' Tnii - (4} Z .1 ac! C} frangfiorg flo‘i‘ Passl’diflrtf, (c) Find the particular solution that satisfies the initial condition {of}: pan.) 2 [2,1]} . “1| VEH'ZJ: gal-{it'E-Q —_: [H {‘23: _.2- +Kh‘j :9 A. 2': / _ - a: - _Z on; its—o Wit = 4 CL ‘3 +itxfil. :i _ tor—O .Unc/‘ffiiéflfifimal "425235731?! fi%5_.__?3_ ...
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This note was uploaded on 02/08/2011 for the course MATH 225 taught by Professor Staff during the Fall '08 term at Mines.

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AK-MATH225F09-WS5 - MATHEEE, Fall EUDQ Name: k Worksheet 5...

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