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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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7 , if ï 4k or ï 4k 1
4. 7 0 7 has no limit as ï
^ | —ó0, if ï = 4k - 2 or ï = 4k - 3; Óï
5. 7ï = (0.5)ï(70 - 12) + 12; óï ^ 12 as ï ^æ
6. 7ï = (-1)ï(0.5)ï(70 - 4) + 4; óï ^ 4 as ï ^æ
7. 7.25% 8. \$2283.63 9. \$258.14
See SSM for 10. (a) \$804.62 (b) \$877.57 (c) \$1028.61
detailed solutions 11. 30 years: \$804.62/month; \$289,663.20 total 20 years: \$899.73/month;
to 10, 13, 14, 17, \$215,935.20 total
17a 12. \$103,624.62 13. 9.73%
16. (b) u --- ---æ as n --- æ
17b, 18 19. (a) 4.7263 (b) 1.223% (c) 3.5643 (e) 3.5699
Miscellaneous Problems, page 126
1 - 7
8-32
1. ó = (c/x2) + (x3/5) 2. arctan(y/x) --- ln ^ x2 + y2
3. x2 + xy- 3 y - y3 = 0 4. x = cey + ye-7
5. x2 Ó + xy2 + x = c 6. ó = x---1 (1 --- e1---x)
7. ( x2 + y2 + 1 ) e- y 2 = c 8. y = ( 4 + cos 2 - cos x)/ x2
9. x2 ó + x + y2 = c 10. (f/x3) + (y/x2) = c
11. x3/3 + xy + ey = c 12. ó = ce x + e x ln(1 + e?)
13. 2(y/x)1/2 --- ln |x| = c; also y = 0 14. x2 + 2xy + 2 y2 = 34
15. ó = c/cosh2 (x /2)
16. (2/\/3) arctan[(2y --- x)/\/3x] --- ln |x| = c
17. y 18. 2
II y = cx x
c
3
1
e2
19. 3 ó --- 2xy3 --- 10x = 0 20. ex + e y = c
21. e---y/x + ln |x| = c 22. y3 + 3 y x3 + 3 x = 2
- ë 2 x
23. 1 e2x also y = 0 24. sin2 x sin ó = c
25. 26. x2 + 2x2 ó --- ó2 = c

27. sin x cos 2ó --- 2 sin2 x = c 28. 2xy + xy3 --- x3 = c
29. arcsin(y/x) --- ln |x| = c; also ó = x and ó = ---x
30. xy2 --- ln |y| = 0
31. x + ln |x| + x + ó --- 2ln |y| = c; also ó = 0
32. x3 y2 + xy3 = ---4
CHAPTER 3 Section 3.1, page 136
3, 5, 7, 10, 15
17, 19, 21
9
10
11
12
13
14.
v= c,et + c~ e
y = 2
+ c2e
-t/3
— t —21
Ó = c1 e + c2e
y = c1et/2 + c2et
c2e
3t/2
2.
4.
5. y = c1 + c2e^t 6. y = c1e3t/2 +
7. y = c1 exp[(9 + 3V5)f/2] + c2 exp[(9 — 3j5)t/2]
8. y = c1 exp[(1 + \/3)t] + c2 exp[(1 — \/3)t]
y —— æ as t —— æ
3t • " — 0 as t — æ
y — —æ as t — æ y =—1 — e—3t ; y —— 1 as t —æ
y = 26 (13 + 5VT3) exp[( 5 + v/T3)t/2] + ^(13 — 5VTI) exp[(—5 — VT3) t/2];
y — 0 as t — æ
y = (2/V33) exp[( 1 + V33)t/4] — (2/Ó33) exp[(—1 — v/33)t/4]; y — æ as t — æ
y = et;
y = 2e—t — 2e ¦“• y-
y = 12et/3 — 8et/2;
-3t
—9(t — 1) , 9_ t—1.
+ 10 e •
y (t+2)/2.
¦> æ as t — æ y — —æ as t -
OO
15. Ó = TO e
16. y =—ie(t+2)/2
17.
19.
20. y = — et + 3et/2; maximum is y = 4 at t = ln(9/4), y = 0 at t = ln9
Ó' + Ó — 6 y = 0
18. 2/' + 5Ó + 2y = 0
ó = 4et + e t; minimum is y = 1 at f = ln2
21. a = -2
22. â = —1
688