{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HWK Answers not in book

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

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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)]. ...
View Full Document

{[ snackBarMessage ]}