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# Elementary Differential Equations and Boundary Value Problems - Boyce W.E.

Boyce W.E. Elementary Differential Equations and Boundary Value Problems - John Wiley & Sons, 2001. - 1310 p.
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(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 7 > 0; undefined for 7 < 0 6. Converge for 7 > 0; diverge for 7 < 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 7at t = 0.8 is between 5.5 and 6. No reliable estimate is possible at t = 1 from the specified data.
686
See SSM for detailed solutions to 18, 22.
1, 4a
4c, 7
11
17. A reasonable estimate for ó 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. d w/ds = 1 — (w + 3)3, w(0) = 0
n 2k tk
3. (a) Ôï(t) — Ó) — (c) lim ôï(t) = º2' - 1
11 j—* k! ï^æ ë
õïë (-1)ktk
4. (a) Ôï(t) = ^ —û--------------- (c) lm ôï(t) = e - 1
11 k! ï^æ 11
k=1 Ë‘
5. (a) ôï(t) = ? (-1)k+1tk+1/(k + 1)!2k—1
k=1
(c) lim ôï(t) = 4e-t/2 + 2t — 4
ï^æ ï
^ï+1 ï t2k—1
6. (a) ô (t) = t------------------ 7. (a) ô (t) = V --------------------------
(ï + 1)! 1 • 3 • 5 ,..(2k - 1)
(c) lim ôï(t) = t
ï^æ ï ï t3k-1
8. (a) ô (t) = — -----------------------
k=1 2 • 5 • 8 •••(3k - 1)
t3 t3 t7 t3 t7 2t11 t15
9. (a)ô-, (t) — —; ôî(') —---------+------; ô^(') —------------+------+-------------------+---------î-----
1 3 2 3 7 • 9 3 3 7 • 9 3 • 7 • 9 • 11 (7 • 9)2 • 15
t4 t4 3t7 3t10 t13
10. (a) ô³ (t) — t; ô9 (t) — t — —; ô3 (t) — t —---------+------—--------------+--------
n 4 È3 4 4 • 7 16 • 10 64 • 13
t2 t4 t6 7
n. (a)ô1(t) = t, ô2(t) = t — — + —— — + î(t x
t2 t3 t4 7t5 14t6 ^ 7
ô.(0 = t-----------1---------1------------1---------+ î (t7),
3 2! 3! 4! 5! 6!
t2 t3 7t5 3116
-----+ — —--------+ ----
2! 3! 5! 6!
12. (a) ô(') = -t - t2 -
ô4(t) = t -L- + ^- ^ã + Öã+ î (t1)
t3
2
t2 t3 t4 t5 t6
ô() = -t---------------1------1----------------------+ O (t1),
È2 2 6 4 5 24
t2 t4 315 4t6
ôÌ) = -t - - + - - — + — + O(f),
ô3() 2 12 20 45 ( ),
t2 t4 7t5 t6
— + — — — + —
2 8 60 15
Section 2.9, page 124
ô4(t) = -t - Ò + 7Ã-777 + 77 + O (t1)
1. 7n = (-1)ï(0.9)ï70; 7n ^ 0 as ï ^æ
2. 7ï = 70/(ï + 1); 7ï ^ 0 as ï ^æ
3. 7ï = 70V(ï + 2)(ï + 1)/2; óï ^æ as ï ^æ
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