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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.
Download (direct link): elementarydifferentialequations2001.pdf
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9. y = c1cos2x + 1 cos x 10. y = 2 cos x
11. Xn = [(2n - 1)/2]2, yn (x) = sin[(2n - 1 )x/2]; n = 1, 2, 3,...
12. Xn = [(2n - 1)/2]2, yn(x) = cos[(2n - 1)x/2]; n = 1, 2, 3,...
13.
X0 = 0,
y0(x) = 1; Xn = n , yn(x) = cos nx; n = 1, 2, 3,...
14. Xn = [(2n - 1)๏/2 L]2, yn (x) = cos[(2n - 1)๏ x/2L]; n = 1, 2, 3,...
15. X0 = 0, y0(x) = 1; Xn = (nn/L)2, yn(x) = cos(nnx/L); n = 1, 2, 3,
16. Xn = - [(2n- 1)n/2L]2, yn (x) = sin[(2/7 - 1)n x/2L ]; n = 1, 2, 3,...
Section 10.2, page 555
1.
3.
5.
7.
9.
10.
11.
T = 2n/5 Not periodic T = 1 T=2
f (x) = 2L - x in L < x < 2L;
2. T = 1 4. T = 2L 6. Not periodic 8. T = 4 f (x) = —2L - x in -3L < x < -2L
f (x) = x - 1 in 1 < x < 2; f (x) = x - 8 in 8 < x < 9
f (x) = - L - x in - L < x < 0
2L
(-1)n
13. (b) f(x) =—T)
TT ‘ J
1 2
14. (b) f(x) = 2 - -J2
n=1
15. (b) f(x) = -- + ?
L
sin[(2n - 1)n x/L] 2n — 1
n=1
2cos(2n - 1)x (- 1)n+1 sin nx
n(2n - 1)2
1 4 cos(2n - 1)nx
16. (b) f(x) ^------2—
-2 ฯ=1 (2n - 1)2
2
3L
n=1
17. (b) f(x) = — + J2
TO
18. (b) f(x) = J2
2L cos[(2n - 1)nx/L] (-1)n+1 L sin(nnx/L)
(2n - 1)2n2 nn
n=1
2 nn j 2
------cos -ใ- + —
nn 2 \nn
4 sin[(2n - 1)nx/2]
19. (b) f(x) =
n=1
2n 1
2 ^ (-1)n+1
20. (b) f (x) = — ำ -----------------sin nnx
าร ‘ J n
n
2
2
2
Answers to Problems
725
See SSM for detailed solutions to 27a
2ab, 4a
4b, 7abc
2 8 ^ (-1)๋ nnx
21. (b) f (x) = —ณ----------t 7 2— cos------
3 ๏2 ฯ=1 n2 2
1 12 ๆ cos[(2n - 1)๏x/2] 2 ^ (-1) . nnx
22. (b) f (x) = - +---------2 > -------------------^--------ณ---> -----------sin -
- ห ^ (2n - 1)2 ๏ ^ "
2
n=1
n=1
2
11 1 23 (b) f(x) = 12 + ^5
(-1)n - 5 nnx
------2----- cos ------
n2 2

4[1 - (-1)n] (-1)n
9
24. (b) f (x) = 8 +J2
162[(—1)n - 1] 27(—1)n
nn x 108(—1) + 54 nn x
-------> ----------3—T----- sin-----
3 „็„็ ็
25. m = 81
26. m = 27
28. ? f (t) dt may not be periodic; for example, let f (t) = 1 + cos t. Section 10.3, page 562
4 sin(2n — 1)๏ x
1. (a) f(x) = -J2'
n=1
๏ x—v
2. (a) f (x) = - - X
n=1
L 4 L 1
2n - 1 2
(-1)n
2 cos(2n — 1)x +-------------sin nx
3. (a) f(x) = - + 2

_ (2n — 1)2๏
cos[(2n — 1)๏x/L]
n=1
(2n - 1)
2
2 4 ^ (-1)n+1
4. (a) f(x) = —ณ---------2 > -------็— cos nnx
3 ๏2 ^ n2
n-1
5. (a)
6. (a)
1 2 (— 1r
f (x) = ๒ + - ำ] -------------T cos(2n - 1)x
2 ๏ “ 2n — 1
n=1
^0 ^—\
f (x) =--------+ > (an cos nn x + bn sin nn x)
2 n=1
1 2(—1)n
= ็, 3n =
22 n n
๊ =
— 1 / nn,
1 /nn - 4/n3n3, n odd
7. (a) (b)
n = 10 n = 20 n = 40
n=1
1 — cos nn (—1)
--------;---- cos nx------------sin nx
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