HW12_-_Tenali

# HW12_-_Tenali - ANSWERS FOR SELECTED ODD-NUMBERED PROBLEMS...

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Unformatted text preview: ANSWERS FOR SELECTED ODD-NUMBERED PROBLEMS 9 CHAPTER 7 ANS-IO 0 ANSWERS FOR SELECTED ODD-NUMBERED PROBLEMS sin(\//Tl) Wt _ ‘ x (—1)" n_ cosh/XI) “O’NEQMMW%V_ r (C) y = Clx sin<ﬂ> sz cos Y x — y (—1)” 2n _ 33. (b) yl(t) — "go—man + I)! (V711) EXERCISES 6.3 (PAGE 250) 1- 3’ = CIA/306) + CzJ—1/3(x) 3- y = €1J5/2(X) + 021—5006) 5 y = 6110(x) + 0217006) 7 y = c1J2(3x) ‘I‘ c2Y2(3x) 9 y = 0112/3536) + 02J~2/3(5x) 11 y = clx‘llle/gmx) ‘I’ c2x_1/2J-1/2(ax) 13 y = x71” [clJ1(4x1/2) + c2Y1(4x“2)] 15 y = XICIJ1(X)+ 621/100] 17 y = x1” ICIJ3/2(x) + 62 Y3/2(x) 19 y : x—1[C1J1/2(%x2) + C2J_U2(%X2)] 23 y = 351/2 [CIA/206) + CzJ—i/2(x)] = C1 sinx + C2 cos x 25 y — le/2[C1Jl/2(‘é‘x2) + C2]-]/2(%x2)] = Clx‘3lzsin(§x2) + sz‘mcoszQ) 35 y : ClxI/2J1/3(§’ax3/2) + C2X1/2J_1/3(% ax3/2) 45 P206), P3(x), P4(x), and P5(x) are given in the text, P600 = “15(231x6 — 315x4 + 105x2 _ 5), P7(x) = {6(429x7 — 69325 + 315x3 — 35x) 47 A1=2,A2=12,A3:30 CHAPTER 6 IN REVIEW (PAGE 253) 1 False 1 1 3 2:2 7 x2(x-1)y”+y’+y=0 9 r1:%,r2:0 y,(x) = ClxI’ZII — %x + \$22 -' \$29 + - - y2(x) = C2[1— x + é-xz 91—0x3 + ‘ ' 11 yl(x) = co[1+%x2 + £x3 +3261 + ' - y2(x)=cl[x+%)t3+; 4+ - - 13 71:3,1’2:0 nm=cwh+ﬁ+\$f+ﬁf+~1 y2(x) = C2[1 + x + %x2] 15 y(x) = 3[1——x2 + gx“ ﬁxé + - - -] —2[—5Hgﬁ—ﬁﬂ+ ] 17 g7; 19 x = 0 is an ordinary point 1 1 21. y(x)—co[1 39+ 2 Z’xé 33 3,9 I ‘ I 1 . + .___J4+ 7 Cll:l Y 4 7x EXERCISES 7.1 (PAGE 261) 2 1 1 1 —e”‘—- 3 — s s s 5 1+?“ sz+l 13 15 17 19 —— 21 ——— 23 25 27 1 29 c7 + 31 s —kI ﬁ‘ 5— ’2(s—2)”2§ s2+16 4003 5 + (sin 5)s 3 s2+16 EXERCISES 7.2 (PAGE 269) 1,.th 3 r— 22‘“ §1+3r+§ﬁ+g§ 7r-1+e2’ 9 if!” 11 \$51117; 13 cos - 15 2 cos 3t — 2 sin 3t 17 g %e_3’ 19 21 1.0 3e0'“ + 0.6e—0-2' 23 5e” — at + 1e6' 25 gcos \/§t~ ' 27. —4 + 32”1 + cost + 3 sint 29 smt — ésin 2t 31 1 y 33. y = 1064’ + :36 6’ 35 y = g6” - %e_4’ ANSWERS FOR SELECTED ODD—NUMBERED PROBLEMS 0 37. y =1OCost+ 231111— V2sin V21 39. y = —§e””2 + ée‘z’ + nge’ + ée" 41. y = ﬁe" — ie”3’cos 21 + if” 511121“ EXERCISES 7.3 (PAGE 278) 1 6 1.———-— . (s - 10)2 3 (s + 2)4 5. 1 2+ 2 2+ 1‘ 7.——3——- is» (s—2) (5—3) (3—4)2 (s—1)2+9 9. S 5—1 s+4 +3 (s~1)2+25 (s+4)2+25 13. 63’ sin I 17. e" - re" 32 + 25 11. £126?” 15. [2’ cos 1 — 2?” sin 1 19. 5 — r - Se" — 416" - \$126" 21. y = te'4’ + 28‘“ 25. y = 51+ 527 — £6” + \$1? 23. y = e" + 21‘6" 27. y = —%e3’&in 2r ‘ x 29.y=%—le’cost+%e’sint 5 31. y = (e + 1)fe_’+ (e — 1)e_’ 33. 2(1) = - 2e"7”zcos ﬁt — 7VBe‘7”2 sin VB! 2 2 10 6‘1 e—2s e—Zs 37. y 39. S2 + 2 S S —7rs l _ 2 _ 41. \$2 + 4e 43. 2(1‘ 2) 011(1 2) 45. —sin102£(t — 7T) 47. 011(z- 1) — e-<'-I>021(z- 1) 49. (c) 51. (f) 53. (a) ‘ 2 4 _ ‘ 55. fa) : 2 — 4210— 3); \${f(r)} = E — Ee 3* 57. ﬁt) = 8210— 1); \$971)} .—. 2% + 2 _2 + e— .S‘ S S 1 e—Z: e-Zs 59. f(1) = t — 1021(1— 2);.f£{f(t)} = 3 — 2 - 2 S S S —as wbs 61.10) = 2m — a) — 02w — 1913110)} = — e 63. y = [5 — sew-1)] 0110 ~ 1) 65. y 2 —§— + )1 + ge—Z’ —§021(z — 1) — 5(1 — 1) 011(1 - 1) +§e-2<r-1>0u(t— 1) 67. y = cos 2: — gsin 2(t — 277) 0210 :— 277) + %s1n(t — 277) 0110 — 271') 69. y = sint + [1 — cos(t — 77)]0210 — 7T) — [1 — cos(r — 277)] “110‘ — 271') 71. m) — 31 156511141 3(1 5) 021(2 5) ‘v 1 33311140 5) 02m 5) {3 011(1 5) + 27500340 — 5) 021(1 — 5) ANS-11 73. q(t) = 3716 — 3) — 97507310210: — 3) 1 1 10 75. (a) 111) = jazz—10’ — WCOST + 'l—O—lsinf _ ﬂe~10(1—3m2)%<t _ 101 2 + -1—0—cos<t — 021<1 — 101 2 2 1 , < 377) < 377) +——-s1nt—-— 0251—— 101 2 2 WOL2 WOL wo 77. - = 2 — —— -3 A W) 16EIA 12EI“‘ 24E1A wo L 4 < L) _ __ ._ O” J _ _ 24E1<x 2> Y 2 79. m) = We” 2 “’0L .3 48E1x_24E1" w0 5L 4 5 < L>5( L) + —— — + .—— -—— 60EILLZX A Y 2 q” 2 81. (a) :1:=k(T 70 57.51 (230 57.51)oll(t—4)) EXERCISES 7.4 (PAGE 289) 1 1 3 s2 — 4 ‘ (s + 10)2 ' (s2 + 4)2 5 6s2 + 2 7 12s ~ 24 ' (s2 — 1)3 ‘ [(s — 2)2 + 36]2 —_l ~1 l -1 l ' 9.y— 2e +Zcosr chosr+zts1nt 11. y = 200331+§sin3t+étsin3t 13. = ﬁsin4t + \$181114: 416 — 77) sin 4(1 — 77)021(z- 77) 6 17. y=§13+c112 19. —5 ' s 21. ______S_—_1_______ 23. 1 (s + 1)[(s - 1)2 + 1] 5(5 _ I) S + 1 1 25- --~—-—-- 27. —— s[(s + 1)2 + 1] 52(S w 1) 352 + 1 . 29. -—-—-——-—- 31. !_ s2(s2 + 1)2 e 1 33. e’ — 112 —r— 1 37. fo) = sint 39. f0) : —§'e" + get + gre’ + ﬁzze’ 41. ﬁt) = e" 43.f(1 = gem + ée‘g’ + gees 21+ ism 2: ANSWERS FOR SELECTED ODD—NUMBERED PROBLEMS ' CHAPTER'7 ...
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## This note was uploaded on 03/02/2011 for the course MATH 1101 taught by Professor Tenali during the Spring '11 term at FIT.

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HW12_-_Tenali - ANSWERS FOR SELECTED ODD-NUMBERED PROBLEMS...

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