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Elementary differential equations 7th edition - Boyce W.E

Boyce W.E Elementary differential equations 7th edition - Wiley publishing , 2001. - 1310 p.
ISBN 0-471-31999-6
Download (direct link): elementarydifferentialequat2001.pdf
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2. (a) 1.1, 1.22, 1.364, 1.5368
(b) 1.105, 1.23205, 1.38578, 1.57179
(c) 1.10775, 1.23873, 1.39793, 1.59144
(d) 1.1107, 1.24591, 1.41106, 1.61277
3. (a) 1.25, 1.54, 1.878, 2.2736
(b) 1.26, 1.5641, 1.92156, 2.34359
(c) 1.26551, 1.57746, 1.94586, 2.38287
(d) 1.2714, 1.59182, 1.97212, 2.42554
4. (a) 0.3, 0.538501, 0.724821, 0.866458
(b) 0.284813, 0.513339, 0.693451, 0.831571
(c) 0.277920, 0.501813, 0.678949, 0.815302
(d) 0.271428, 0.490897, 0.665142, 0.799729
5. Converge for y > 0; undefined for y < 0 6. Converge for y > 0; diverge for y < 0
7. Converge
8. Converge for |y(0)| < 2.37 (approximately); diverge otherwise
9. Diverge 10. Diverge
11. (a) 2.30800, 2.49006, 2.60023, 2.66773, 2.70939, 2.73521
(b) 2.30167, 2.48263, 2.59352, 2.66227, 2.70519, 2.73209
(c) 2.29864, 2.47903, 2.59024, 2.65958, 2.70310, 2.73053
(d) 2.29686, 2.47691, 2.58830, 2.65798, 2.70185, 2.72959
12. (a) 1.70308, 3.06605, 2.44030, 1.77204, 1.37348, 1.11925
(b) 1.79548, 3.06051, 2.43292, 1.77807, 1.37795, 1.12191
(c) 1.84579, 3.05769, 2.42905, 1.78074, 1.38017, 1.12328
(d) 1.87734,3.05607,2.42672, 1.78224, 1.38150, 1.12411
13. (a) —1.48849, —0.412339, 1.04687, 1.43176, 1.54438, 1.51971
(b) —1.46909, —0.287883, 1.05351, 1.42003, 1.53000, 1.50549
(c) —1.45865, —0.217545, 1.05715, 1.41486, 1.52334, 1.49879
(d) —1.45212, —0.173376, 1.05941, 1.41197, 1.51949, 1.49490
14. (a) 0.950517, 0.687550, 0.369188, 0.145990, 0.0421429, 0.00872877
(b) 0.938298, 0.672145, 0.362640, 0.147659, 0.0454100, 0.0104931
(c) 0.932253, 0.664778, 0.359567, 0.148416, 0.0469514, 0.0113722
(d) 0.928649, 0.660463, 0.357783, 0.148848, 0.0478492, 0.0118978
15. (a) —0.166134, —0.410872, —0.804660, 4.15867
(b) —0.174652, —0.434238, —0.889140, —3.09810
16. A reasonable estimate for y at t = 0.8 is between 5.5 and 6. No reliable estimate is possible at t = 1 from the specified data.
686
Answers to Problems
See SSM for detailed solutions to 18, 22.
1, 4a
4c, 7
11
17. A reasonable estimate for y at t = 2.5 is between 18 and 19. No reliable estimate is possible at t = 3 from the specified data.
18. (b) 2.37 < a0 < 2.38 19. (b) 0.67 < a0 < 0.68
Section 2.8, page 113
1. d w/ds = (s + 1)2 + (w + 2)2, w(0) = 0
2. dw/ds = 1 - (w + 3)3, w(0) = 0
n 2k tk
3. (a) 0n(t) = T2 (c) lim Sn(t) = e2' - 1
11 j—s k! n^TO "
% (-1)ktk
4. (a) 0n(t) = ^ —T, (c) lim 0n(t) = e - 1
11 k! n^TO 11
k=1 A‘
5. (a) 0n(t) = ? (-1)k+1tk+1/(k + 1)!2k-1
k=1
(c) lim 0n(t) = 4e-t/2 + 2t - 4
n^TO n
tn+1 n t-k-1
6. (a) 0 (t) = t 7. (a) 0 (t) = V -
(n + 1)! Ar 1 • 3 • 5 •••(-k - 1)
(c) lim Sn(t) = t
n^TO n n t3k-1
8. (a) 0 (t) = - ------------------------------
k=f - • 5 • 8 ???(3k - 1)
t3 t3 t7 t3 t7 2t11 t15
9. (a)0i (t) — —; S-(t)----------—---------+-; 03(t) —-----+----------+--------------+----------------------------o-
w^w 3, Y^W 3 7 • 9 Y^w 3 7 • 9 3 • 7 • 9 • 11 (7 • 9)2 • 15
t4 t4 3t7 3t10 t13
10. (a) 01 (t) — t; 0- (t) — t — —; 03 (t) — t —--------+----------—--------+---------
n 4 ^ 4 4 • 7 16 • 10 64 • 13
t2 t4 t6 7
n. (a)01(t) = t, 02(t) = t — — + —— — + o(t),
t2 t3 t4 7t5 14t6 7
03(t) = t 1--------------1--------------1-------+ O (t7),
3 2! 3! 4! 5! 6!
t2 t3 7t5 31t6
+ — — + -----------------
2! 3! 5! 6!
12. (a) 01(t) = -t - t2 -
<%) = t -L- + T;-^r + ^r+ O (t7)
t3
2
,2 3 ,4 t5 16
02(t) = -t 1------------------1------------------------+ O (t1),
^ 2 6 4 5 24
t2 t4 315 4t6
M) = -t - - + - - — + — + O{f),
Y3( ) 2 12 20 45 (
t2 t4 1t5 t6
+ — + —
2 8 60 15
Section 2.9, page 124
$4(t) = -t -L-+L--^: + ^+ O (t1)
1. Yn = (-1)"(0.9)% Yn ^ 0 as n ^ro
2. yn = 7p/(n + 1); 7n ^0 as n ^ro
3. yn = 70V(n + 2)(n + 1)/2; yn ^ro as n ^ro
f y„, if n = 4k or n = 4k — 1; .
4. y = { 0 ,, „ y has no limit as n -> oo
^ | —y0, if n = 4k - 2 or n = 4k - 3; ^
5. yn = (0.5)n(y0 - 12) + 12; yn ^ 12 as n ^ro
6. yn = (-1)n(0.5)n(y0 - 4) + 4; yn ^ 4 as n ^ro
1. 1.25% 8. $2283.63 9. $258.14
Answers to Problems
See SSM for detailed solutions to 10, 13, 14, 17, 17a
17b, 18
1 - 7
8 - 32
CHAPTER 3
3, 5, 7, 10, 15
17, 19, 21
10. (a) $804.62 (b) $877.57 (c) $1028.61
11. 30 years: $804.62/month; $289, 663.20 total 20 years: $899.73/month;
$215,935.20 total
12. $103,624.62 13. 1.73%
16. (b) u — —to as n — to
19. (a) 4.7263 (b) 1.223% (c) 3.5643 (e) 3.5699
Miscellaneous Problems, page 126
1. y = (c/x2) + (x3/5) 2. arctan(y/x) - ln y7x2 + y2
3. x2 + xy — 3 y — y3 = 0 4 x = ce7 + ye7
5. x2 y + xy2 + x = c 6. y = x-1(1 - e1—x)
7. (x2 + y2 + 1)e-y2 = c 8. y = ( 4 + cos 2 - cos x)/ x2
9. x2 y + x + y2 = c 10. (f/x3) + (y/x2) = c
11. x3/3 + xy + ey = c 12. y = ce x + e x ln(1 + )
13. 2(y/x)l/2 - ln |x| = c; also y = 0 14. x2 + 2xy + 2 y2 = 34
15. y = c/cosh2 (x /2)
16. (2/V3) arctan[(2y - x)/V3x] - ln |x| = c
17. y = ce3x - e2x 18. y = cx- - x
19. 3 y - 2xy3 - 10x = 0 20. ex + e-y = c
21. e—y/x + ln |x| = c - rt 2 v 22. y3 + 3 y - x3 + 3 x = 2
23. 1 e2x — = - x I dx + cx; also y = 0 24. sin2 x sin y = c
25. y2 x2 x/ y + arctan(y/x) = c 26. x2 + 2x2y - y2 = c
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