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 .. 393 394 395 396 397 398 < 399 > 400 401 402 403 404 405 .. 609 >> Next

21. f (x) = +-----.--------------------------------
" r2 j=1 (2n - 1)2
2
22. f(x) = ^ sin(n-x/L)
n1
1 X 2 n 4 / n-
23 (a) f (x) = T + - sin T" + T (cos T
4 - n 2 n2 2
n=1 L
-TO (-1)n
24. (a) f (x) = 2 > -------------------sin nx
' 11
25. (a) f(x) =
4n22(1 + cos n) 16(1 cos n)
+
4 16 1 + 3 cos n n x
26. (a) f (x) = - + ---------2-------cos
3 7=1 n2
3 6 1 cos n
27. (b) g(x) = - + > ----------------------2--------cos
/ Z----4 11
2 2 n 1 ... 6 -TO 1 n x
h(x) = > sin
n
n=1
4 n x
3
1 TO
28. (b) g(x) = 4 + X
4cos (n/2) + 2n sin (n/2) 4 n x
------------------------------------cos-------
n22 2
4 sin(n/2) 2n cos(n/2) n x
h(x) = > ------------------------------------sin
22
n22
5 ^ 12cos n + 4 n x
29. (b) g(x) = -- + ?----------------^2-------------cos.
h(x) = -21]
n=1
TO ~2_2
2
1 n 2(3 + 5cosn) + 32(1 cosn nx
n=1
2
1 TO
30. (b) g(x) = 4 + J2
6n22(2cosn 5) + 324(1 cos n) n x
, ------------------------------------cos----
4 n44 3
h(x) =
4cos n + 2 144 cos n + 180
+
n x
40. Extend f(x) antisymmetrically into (L, 2L]; that is, so that f(2L x) = f(x) for
0 < x < L. Then extend this function as an even function into (2L, 0).
Section 10.5, 579
1. xX"- XX = 0, T + XT = 0 2. X"- XxX = 0, T + XtT = 0
3. X" - X(X' + X) = 0, T + XT = 0 4. [jo(x)X']' + Xr(x)X = 0, T" + XT = 0
5. Not separable 6. X" + (x + X)X = 0, Y" XY = 0
7. u(x, t) = e-4002f sin2 x - 2e-25002f sin 5x
8. u(x, t) = 2e- f/16 sin( x/2) e- f/4 sinx + 4e- f sin2x
100 1 cos n 22,,1 n x
9. u(x, t) = --e-n f/1600 sin -
n
n=1
40
nx
cos
2
2
33
n
728
Answers to Problems
See SSM for detailed solutions to 10
15abcd, 18a
18b, 19b, 20, 22
3, 7, 9abd
12abcd
14abc
1UU xv
10. u(x, t) = -tJ2
160 ^ sin(nn/2) e_n2n2t/1600 sin nnx
40
2
n=1
100 cos(nn/4) - cos(3nn/4) -n2n2^1600 nnx
n 40
80
12. u(x, t) = ^2
80 (-1_)+1 e-n2n21/1600 sin nn x
n 40
13. t = 5, n = 16; t = 20, n = 8; t = 80, n = 4
14. (d) t = 673.35 15. (d) t = 451.60 16. (d) t = 617.17
17. (b) t = 5, x = 33.20; t = 10, x = 31.13; t = 20, x = 28.62; t = 40, x = 25.73;
t = 100, x = 21.95; t = 200, x = 20.31
(e) t = 524.81
200 1 cos nn 22,*2, nn x
18. u(x, t) = ------V-----------------e-n n a 1 /400 sin-----
n n 20
(a) 35.91C (b)67.23C (c) 99.96C
19. (a) 76.73 sec (b) 152.56 sec (c) 1093.36 sec
21. (a) awxx - bwt + (c - b5)w = 0 (b) & = c/b if b = 0
22. ^" + /X2^ = 0, " + (X2 - /2) = 0, T + a2X2T = 0
X
Previous << 1 .. 393 394 395 396 397 398 < 399 > 400 401 402 403 404 405 .. 609 >> Next