Sect3.4 - ' GS’quzIn‘hrb D.E . Wait: In problems 8)...

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Unformatted text preview: ' GS’quzIn‘hrb D.E . Wait: In problems 8) ,i-3 HJ 18) / cf b is U-Seo‘ Ck. abo'epeqo/eqé an'qble. .47 “Me beak bob K is > _ 03:90] he/z, » (Z) U96 Eumls fiormulnh wlmwe expressdy- as. out—Sb. exp (2-3:) Expand 115mb Eqdoy‘s Qofmula '. e“ = Cos'x. * IIsz . exp (2-36 = €Xp(23 ° 914303;) 2 81%“ 4M] = (e'cbscsy-ue'smtsfi (8) FW W Ward gawk“ of, s. 3” "' 23’ t- (“a = o, T‘E 300‘; e" 3 p‘ug ado b.E.’. e"‘(r’--Zr+a=o => p='EE___—W= {IE-Ii 2. (Hfi‘afix (pg—1);! 3? ‘3(1)= Q‘e ** ale .1 21?: n vz‘fs’x " 3m: c‘e e + ate 9 3m = 6.6‘ [Cos Ex + ismfiz] * czé‘ECos Rx dumfi'a; 3(1) s (cu-cg 9" cos 5‘1, * (cpcgie‘sm fi’x W W 6.3 Ca '1- ' - t . 3 C36 COSTS—‘1. ‘V Cg 8 Sun fix, . 3 (1°) Fwd W 3mm: We»: 3'5 (332% = O . Trg gm: e“; #443 min max. 1-22 q-B . e”[r‘*z.~+21=o =5 F: . = 4m ' 2 («new -..i -' ‘ , -' a? a“): c'e f c at I )1- ‘, 6.31:er * Czexeu t. .1 ’ ,3 ‘ = c,o [easxu‘smz] + ate [cosx-zsmq _ ‘5“) = (38.1005! + CV easz (H3 Fund %2 3mm! solulcm‘. 3"+63' *- 138 =0. Trfi aw) -.- e“; ud'o DES CrxLPz+bra-l31=o é f‘: -———-——-——-: -Stzi 93*?‘37‘ (-s-zth. g 15(1): c '31 “28) '3! '1‘?!) i +Cze = Q8 6 *cte 6 3(1) = C‘C—u 21» {Sun 61.1 1- czéhiws 62- igm 2;} . '3‘. ~31. 3m= £38 coszx + cqe smu Fuid \Lhe Sotwhm 06 We IVP; 8’6ch 14: flrapk J desach 11‘s behalva as r inc/vases. 3'1- =0 3 J ui(o)=0. Trg gm 1‘ 9” J Plus u, e”[_r‘N~S‘1=o 2’? r" “lit-"2°: ~2ti ‘ 'Zx _ ¢ 3(1): ewe “’5 "L " ate,“ Sub-x. Camera) Sud-c» 3(0) a CI ‘ i ""7 300':- c. cosx+ Cain anx 2 _ - - 3 (19‘ = ~23z‘Cosx - 6 Sum - zczeiz" Smx +- Cite?" cosx\ 1L=o Demgirs 05¢“an lad—p.31 1 ~ 8 Sin 27c =3Cx) W W‘ ‘5 '° “3 osccllalm. 'x-wo 5W l Sch/e. Squ+3c4'1-7o,:0 41(0):;2 g’/03;./ Tine. oquosderrs‘lvc eaua‘hon 15 §p¢+ 2P+730 P: —2:* z «5:: N37 3C5) ‘ 3C3) -t/ ‘ "7' 3 ‘EV B 30 b . . ~— é (469: (3,62 coségjéB *‘Ca 6 5'V’C “g . :21 1"71301/7 .6 .27 ‘14:). anbQ/QO’LO' - u/s“ - a ' J ~"6/5 C'fiyéD +C e 3/;16 ,(é3=;2 e, 305 3 3 3: a = C 50 M - “(o I 'l ~ / I ‘He '4» I cam/“0” a [ V ‘ ‘ mi °I . APP/fling f, , *b/é_ EflxcifiCJ-ngfi) .1 '/3 Eu) ~ gze C 5’ (2116): ‘3” 8 Coal g 9/ F D ' v ’ 5 39 “'5/5 ["9 + [ale 6 CosCE’19 L; a 7' ELI C : 5+?) Milo}? ~36 avgcaxl j 9‘ ’7 C93 b vt/ '3 - .1 5 J“ (31645395 C03 @119) +6371 5 SMC'EZE» W7 [‘1 61- A S"; Section 3.4 Problem 24 b > -u:=exp (-t/5) * (2*cos (sqrt (34) *t/5) +7/sqrt (34) *sin (sqrt (34) *t/5 H: n u := C('1/5‘)[2 co > plot({u,0.1,-O.1},t=10. .20); In the picture we see that'the solution, u, stays between the two lines after crossing the bottom one somewhere between 14 and 15. Let’s use Maple to solve for the value of t. > fsolve (u=-O.1,t, 14 . .15); 1451153563 Section 3.4, Problem 27 Problem. Show that W(e’\t cos (at), 6’“ sin (ut)) = new. Solution. One is asked here to calculate the Wronskian of two functions, f (t) = e’“ cos (pt) and g(t) = 6” sin (at). The Wronskian of two functions f (t) and g(t) is: 6’“ cos (at) e"t sin (,ut) Ae’“ cos (pt) —- “6’” sin (pt) Ae’“ sin (at) — Me” cos (pt) So the Wronskian of these functions is (A6” sin (pa—we” cos (lit)) (6"t cos (ut)) — (A6“ cos (pit) — ,ue’V sin (#1)) (eAtsin(pt)). Multiply the terms out and group them by the constant, VA or u in front, and one gets Ae’“ cos (Mt)e’\tsin(,ut) — Ae’“ sin (,ut)e"t cos(,ut) + [1.6” cos (,ut)e’\t cos(ut) + Me” sin (pt) 6” sin(pt). ' Notice the terms with A in front subtract out, While the terms with u in front simplify to (6”)2 cos (#02 + 6"”)2 sin (#02 = (e"‘)2 (cos (Mt)2 + sin (#02) = (e’w)2 = 62M. ...
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This homework help was uploaded on 04/09/2008 for the course MATH 2400 taught by Professor Yoon during the Spring '04 term at Rensselaer Polytechnic Institute.

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Sect3.4 - ' GS’quzIn‘hrb D.E . Wait: In problems 8)...

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