HWK Answers not in book - 252 Answers of the...

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Unformatted text preview: 252 Answers of the even—numbered homework problems Chapter 2 Section 2.2. 1 . I ..: =— 13 . 2.2.: :1— . 222 y 3(113+ ) +6 ‘ 4 y $+c 1 l 2.2. : z . 2.2.8: 3' — y “w — -3=“= . 6y m2+c \\ 318+ 6+6 +38 c 2210- 2 — 1 +6 \\ 2224- “as .. .2y+3m4m+5 ._ .. .y—. 1 11mm?“ -2t . . : m -. .2. : m—~ . 2226 y 28 +2 \\ 2 28 y 21%? 2230- (3.) w 1 (b) —0 (c) — 1 (d) — 2 " ' y_1—c2‘ y"‘ y“1+22' yw2+32 Section 2.3. 2.3.2: yM—mce‘gx (~oo<:r<oo). \\ 2.3.4: yzé—i—ce‘“ (—oo<2<oo). I 2 1 _32 2.3.6: yZEx WE—l-ce (woo<:c<oo). 1 1 11 2.8: m—~2m_ 4-— 2=€~ . 3 y 22: 22: 4+C8 (oo<:c<oo) 3 _2 2 49 2.3.10: y2—2—+c:c (23>0). 2.3.26: $m2y wws—y(y>0). 2.3.28: Tsz+(TD-Tm)em (—oo<:c<oo). 2.3.30: 3; m sinmcosa: — smash-E < :1: < 2.3.32: 3; 21(0 5 3: 31), m 28H — 1 (:1: >1). Section 2.4. 2.4.2: not exact. 1 2.4.4: azsiny+ycoscc——2—y2=c. \\ 2.4.6: not exact. 1 2.4.8: ~y+ylnx+mlna2ma 2.4.10: 3232+xy3=a 2.4.22: ew+my+2y+ye$weym3 2.4.24 E—AK—Ei ' 4y4 2y2 4. 9 2.4.28: #2:? 2.4.30: $2+y2=c(:c+y). 2.4.32: myem+y22xma 2.4.34: 17n(sinm)+y+1ny2=cor ygeysinmmc. 1 2.4.36: 3+ "51132 + Sing w cosy w c (y > 0). Section 2.5. 2.5.2: 232 + 22:3; 2 c. 2.5.4: :3 + 21; 2 egg. 2.5.6: 33% : C(y —:~ 29:). 2.4.8: (y ~ :02 :2 C(y + Sectidn 3.1. 3.1.2: P(10) a: 26,390, _P'(10) z 3658 persons/year. 3.1.4: Po m 201. 3.1.14: T(0) x 64.5 F“. 3.1.20: A(t) = (ft/50. 252 Answers of the evenwnumbered homework problems Chapters 4 82: 5 Section 4. 1. 2 4.1.2: y 2—2-19“ + 56“”. 4.1.4: y : —1——cos:1: — 25inm. 4.1.10: The problem has a. unique solution for ~1r/2 < m < mar/2 4.1.14: (3.) Not possible. (b) Not possible. ((1);; m clm2~(03+3)$4+3. (d) y: ~x2+xé+3 4.1.16: Linearly depended. \\ 4.1.18: Linearly depended. Section 4.2. 4.2.2: 322 m 8””. 4.2.4: y2 = cos(3:r). 4.2.6: 3;; 2 H593. \\ 4.2.8: yr. 2 fl”. 4.2.10: y; = $4. 4.2.18: y 2 cc 4“ 616—33 + Cg. 4 4.2.20: y 2 gm + b— + (326% + age? Section 4.3. 4.3.2: y = c1663" 4 age—6‘”. 4.3.4: y : elem + c262“. 4.3.6: 3; m C§€5m + ewe“. 4.3.8: y t 636(‘2+‘/§)” + CgGlQOJg)m. 4.3.10: y = c1cos(x/\/3) + (:2 sinks/V3). \\ 4.3.30: 3; = —\/3€059 + sin 6. 7 4.3.32: 3; 2 “EN/2 + 14—15342. \\ 2.4.34: 3; = 58“? + 5er. - 1 1 l 2.4. 6: m -— "z —— 29” m ‘34. 3 y 6e + 156 ~+~ we Section 4.4. 4.4.2: y z 31 cos(3x/2)+c2 sin(3m/2)+~g». 4.4.4: y m c1e2m+C2e‘3m—§—~%. 4.4.6: 3; m 343(01 cos(2a:) + c2 sin(2x)) + 542 + 4x + i—bl- ~— 2(33 + 1%»)6". 1 4.4.8: 3; 2 Clem/2 + age—“2 — ELIE-(19 cos(2m) ~+~ 85in(2m)). 4.4.10: 3; 2 (21+ 026""2‘” + £332 + 2:1: «id gxewgw. ' 1 4.4.28: y : gem/2 + “298—250 — 7332 —— 19x — 37. 1 3 . _ W23 _ 3 m 2 —2m 4.4.30. y — (9:v+2)e + (6:1: + 2:1: )8 . 1 1 4.4.32: y 2 Te‘” — 5e’m 4» Zflem ~ 6”) or y = 2 cosha: + 12 sinhm 45938011155. 1 Section 4.6. 4.6.2: y m c1 cosa: + Cg sinm — 005 23111 I seccc + tan 4.6.4: y 2 c; (20313 + (:2 Sims + mcosac — Sinmin 1 cosmf. 4.6.6: y =: 030053: +62 sinzc —1-§-sinx1n|seca:+ tancc|. 1 4.6.8: y 2 age”: + age” + gainhmx). 4.6.16: 3; m 6183”: + age—’36 — Ee'3m(3m + 1). 1 4.6.20: 3; = gem/2 + Ea” - x —- 2. 4.6.22: 3; 2 623(334 — m3 — 23: + 1). Section 4.7. 4.7.2: 3; = x/flcl + (:2 In 4.7.4: y m c; + 0222“. 4.7.6: 3; 2 03:6” —§~ 623:““3. Section 5.1. 5.1.4: m(t)=§sin(4ty/6). \\ 5.1.6: x(t) =~531n(2t). 5.1.22: Equation of motion: ix” + fiw’ ~+~ 2x = 0, m(0) a.— 0, 33(0) '2 5, The solution: 33(t) 2 53364”? The time for the mass to attain its 2 extreme displacement: t9 2 «K. ($’(tg) = 0). The position of x at 5 2 twto: m0) = mag. 5.1.30: (3.) 22(t) 2 e“tcos(2t) + 3sin(2t). 1 e“ . 5.1.32. 32(t) w @(24 + 100i) - 635(24 603(415) + 7sm(4t)). 252 Answers of the even-numbered homework problems Chapters 7 Section 7.1. 7.1.2: 5(1— 73—28). \\ 7.1.4: in ~ 372—3) + 3(1m e—s) .3 .3 32 6"“5 2 s — 1 7.1.12: . 7.1.14: .1.1 3+2 [s~+2)3 7 6 32~23~+~2 28 . .1 ' W. 71 8 (82 +1? Section 7.2. 722‘ \\ 724' 47—— ?fi—l-i \\ 726'1+4t+272 ...6. 3 120. . t4 e2t/5 7.2.8: 4 + E — 678‘. \\ 7.2.10: Mug-h. '\\ 7.2.12: 10 cos(4t). 1 . 7.2.14: 551:. \\ 7.2.15: cos(tx/§) + gamma). Section 7.3. 1 10! 2 2 1 7.3.2: . 7. .4: W. 7.3.6: — . (3+6)2 \\ 3 (8+7)“ (s——2)3 (3-2)2+5—2 s —|— 2 t3e‘ 1 7.3.:——~—-~—. ..12:~————. .. 2—“t' . 8 (8 = 2)2+16 73 6 7314 28 5111(216) 1 . 7.3.16: 2e”3*cos(5t)uge'flsinfit). \\ 7.3.18: 5e27+1otezé t 1 2 1 flea: . . 2: = w —- . . . : m ———-. 732 y 1+e+2te \\ 7324. y 20 3 92: 372 t4 ezt 1373” 7.3.2 : = w — -—-—~ — --- m . 6 y 4 + 8 + 4 + 4. + 4 8 t t . __ m57 __m ~57 - _ 7.3.28. y m 26 cos +10\/§e sm 7 t 7 t 51 t _ . . : z — —-— —— — 2 _ ' 73 30 y 25 + 5 25a cos( 7) -§— 258 5111(215) Section 7.4. - 6 63 I 28(32 —— 3) 7.4.2: . 7.4.4: —————. 7.4. : ~—-———-~. (s w 21)“ \\ (32 w 9)2 \\ 6 (.92 «1: 1)3 2 1... 7.4.8: (8 + 3) 9 7.4.10: 3; : etsint — 156‘ cost. [(3 + 3)? —:— 9]” sint tcost 7.4.12: m 7»: Mm— — . y cos 2 2 7.4.14: 3; = 1 — (1 — sint)u(t —— 73) — at — 3) costu(t m 33). 2 2 2 7420- 2 \\ 7422? —-3-—-—— \\ 7424- 1 ‘ 53(3—1)2' " '(3—2)(362~+~1)' " ‘s2+1 2 s . .2 : WWW. - . . : 74 6 {82+}? \\ 7428 (8%“)? 33+1 2t 8 t mm —' t 7430 5%“)3 \\ 7438 f() 54W58m(\/5) 7.4.40: f(t)m4e“*—7te4*+4tge“‘. \\ 7.4.42: f_(t)w—fcpst+sint. t :3 ' 7.4.44. f(t)—§—§. Section 7.5. 7.5.2: y = 28—15 + e”(t"'1)u(t — I). 7.5.4: isinflitfiflt — 214). 7.5.6: y m cost + sin t[Z/{(t w 21?) ~+ Ll(t — 414)]. ...
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This note was uploaded on 09/26/2008 for the course MA 252 taught by Professor Saito during the Summer '08 term at University of Alabama at Birmingham.

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HWK Answers not in book - 252 Answers of the...

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