Books
in black and white
Main menu
Share a book About us Home
Books
Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics
Ads

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.
Download (direct link): elementarydifferentialequations2001.pdf
Previous << 1 .. 368 369 370 371 372 373 < 374 > 375 376 377 378 379 380 .. 609 >> Next

7 , if 4k or 4k 1
4. 7 0 7 has no limit as
^ | 0, if = 4k - 2 or = 4k - 3;
5. 7 = (0.5)(70 - 12) + 12; ^ 12 as ^
6. 7 = (-1)(0.5)(70 - 4) + 4; ^ 4 as ^
7. 7.25% 8. $2283.63 9. $258.14
Answers to Problems
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 --- --- as n ---
17b, 18 19. (a) 4.7263 (b) 1.223% (c) 3.5643 (e) 3.5699
Miscellaneous Problems, page 126
1 - 7
8-32
1. = (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 + xy2 + x = c 6. = x---1 (1 --- e1---x)
7. ( x2 + y2 + 1 ) e- y 2 = c 8. y = ( 4 + cos 2 - cos x)/ x2
9. x2 + x + y2 = c 10. (f/x3) + (y/x2) = c
11. x3/3 + xy + ey = c 12. = 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. = 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 --- 2xy3 --- 10x = 0 20. ex + e y = c
21. e---y/x + ln |x| = c 22. y3 + 3 y x3 + 3 x = 2
- 2 x
23. 1 e2x also y = 0 24. sin2 x sin = c
25. 26. x2 + 2x2 --- 2 = c


27. sin x cos 2 --- 2 sin2 x = c 28. 2xy + xy3 --- x3 = c
29. arcsin(y/x) --- ln |x| = c; also = x and = ---x
30. xy2 --- ln |y| = 0
31. x + ln |x| + x + --- 2ln |y| = c; also = 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
= 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 as t
3t " 0 as t
y as t y =1 e3t ; y 1 as t
y = 26 (13 + 5VT3) exp[( 5 + v/T3)t/2] + ^(13 5VTI) exp[(5 VT3) t/2];
y 0 as t
y = (2/V33) exp[( 1 + V33)t/4] (2/33) exp[(1 v/33)t/4]; y as t
y = et;
y = 2et 2e y-
y = 12et/3 8et/2;
-3t
9(t 1) , 9_ t1.
+ 10 e
y (t+2)/2.
> as t y as t -
OO
15. = 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
' + 6 y = 0
18. 2/' + 5 + 2y = 0
= 4et + e t; minimum is y = 1 at f = ln2
21. a = -2
22. = 1
688
Answers to Problems
See SSM for detailed solutions to 24, 25a.
Previous << 1 .. 368 369 370 371 372 373 < 374 > 375 376 377 378 379 380 .. 609 >> Next