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 .. 371 372 373 374 375 376 < 377 > 378 379 380 381 382 383 .. 609 >> Next

(b) a = 2
24. Ó2(¥) = f— 2
26. y2(f) = fef
28. y2(x) = x
30. y2(x) = x—1/2 cos x
ds
35. y2(f) = cos f2 37. y2(x) = x—1/2 cos x 41. y= c1 f2 + c2f2ln f
Section 3.6, page 178
1. ó = c1e3f + c2e f — e2f
e f cos2f + c2e f sin2f + 17sin2f— 12cos2f
e3f + c2e—f + 16 fe— f + 3 f2 e— f
+ c2e— 2f + 2f — 2 sin2f — 2 cos2f
cos 3f + c2 sin3f + ^(9f2 — 6f + 1)e3f + 3
e t + c2te t + t 2e t
e— f + c2e— f/2 + f2 — 6f + 14 — -6 sin f — 10 cos f cos f + c2 sin f — 3 f cos2f — §sm2f cos w0f + c2 sin«0f + («2 — w2)—1 cos wf cos rn0f + c2 sinrn0f + (1 /2w0)f sinw0f
e—1/2 cos(\/T5 t/2) + c2e—f/2 sin(vT5 f/2) + 1 ef — 4e— f
2. y = c1
3. y = c1
4. y = c1
5. y = c1
6. y = c1
7. y = c1
8. y = c1
9. u = c 10. u = c
Ï. ó = c 12. Ó = c1
14. ó = ¦Ê sin2f — 19 cos2f + 4 f2 — 1 + |ef 15. ó = 4fef — 3ef + 6fV + 4
4'
e—‘ + c, e2f + 1 fe2f + 1 e
2t
13. ó = ef — 1 e—2f—f — 2
1 +3J
17. ó = 2cos2f— 1sin2f— 3fcos2f
16. ó = º3' + 3e—f— 3e2f —fe2'
18. ó = e— f cos2f + 1 e— f sin2f + fe— f sin2f
19. (a) Y(f) = f(V4 + A ³
+ D sin3f + E cos 3f
(b) A0 = 2/15, A1 = — 2/9, A2 = 8/27, A3 = — 8/27, A4 = 16/81, B0 = — 1/9,
B1 = -1/9, B2 = — 2/27, D = — 1/18, E = — 1/18
20. (a) Y(f) = A0f + A1 + f(B0f + B1) sin f + f(D0f + D1) cos f
(b) A0 = 1, A1 = 0, B0 = 0, B1 = 1/4, D0 = — 1/4, D1 = 0
21. (a) Y(f) = ef(Acos2f + Bsin2f) + (D0f + D1)e2f sin f + (E0f + E1)e2f cos f
(b) A = —1/20, B = — 3/20, D0 = — 3/2, D1 = — 5, E0 = 3/2, E1 = 1/2
22. (a) Y(f) = Ae— f + f(B0f2 + B1f + B2)e— f cos f + f(D0f2 + D1f + D2)e—f sin f
(b) A = 3, B0 = — 2/3, B1 =0, B2 = 1, D0 = 0, D1 = 1, D2 = 1
Answers to Problems
691
See SSM for detailed solutions to 28
30, 33 2
5, 11, 14
18, 22 25, 29
23. (a) Ó(t) = A^ + A11 + A2 + t2(B0t + B1)e2t + (D0t + Ä) sin2t + (E0t + E1) cos2t
(b) A0 = 1/2, A1 = 1, A2 = 3/4, B0 = 2/3, B1 = 0, D0 = 0, D1 = -1/16,
E0 = 1 /8, E1 = 1/16
24. (a) Ó(t) = t(A0t2 + A1t + A2) sin2t + t(B0t2 + B1t + B2) cos2t
(b) A0 = 0, A1 = 13/16, A2 = 7/4, B0 = -1/12, B1 =0, B2 = 13/32
25. (a) Ó(t) = (A0f2 + A1t + A2)e‘ sin2t +(B0t2 + B1t + B2)et cos2t
+ e-t (D cos t + E sin t) + Fet
(b) A0 = 1/52, A1 = 10/169, A2 = -1233/35152, B0 = -5/52, B1 = 73/676,
B2 = -4105/35152, D =-3/2, E = 3/2, F = 2/3
26. (a) Ó(t) = t(A0t + A1)e-t cos2t + t(B0t + B1)e-t sin2t + (D0t + D1)e-2t cos t + (E0t + E1)e-2t sin t
(b) A0 = 0, A1 = 3/16, B0 = 3/8, B1 = 0, D0 = -2/5, D1 = -7/25, E0 = 1/5,
E1 = 10/25 1 0 1 0 1 0
27. y = c1 cos kt + c2 sin kt + ^ [am/(k2 — m2n 2)] sin mn t
m=1
28 _{t, 0 < t < n
. y j-(1 + n/2) sin t — (n/2) cos t + (n/2)en-f, t >n
²1 - 47; e-f sin2t - 1 e-f cos2t, 0 < t < n/2
5 10 5 — — ³
-1 (1 + en/2)e-t cos2t - ^ (1 + en/2)e^t sin21, t > n/2
30. No 33. y = c1e4t + c2e-t - 2e2^
Section 3.7, page 183
1. Ó (t) = e' 2. Ó (t) = -3 te-t
3. Ó (0 = § t2e-t 4. Ó(') = 2t2et/2
5. y = c1 cos t + c2 sin t - (cos t) ln(tan t + sec t)
cos 31 + c2 sin 31 + (sin 31) ln(tan 31 + sec 31) - 1
6. y = c1
7. y = c1
8. y = c1
9. y = c1
10. y = c
11. y = c1
12. y = c1
ñ 2t + c2te 2t - e 2t ln l
cos2t + c2 sin2f + 3 (sin2t) lnsin2t - 31 cos2f cos(t/2) + c2 sin(t/2) + t sin(f/2) + 2[lncos(t/2)] cos(t/2) ef + c2tef - 2ef ln(1 + f2) + tef arctan t
e2f + c2e3f + J [e3(f-s) - e2(f-s)] g(s) ds cos2t + c2sin2t + ³ Ó" [sin2(t - s)] g(s) ds
13. Ó(t) = 1 + f2 ln t 14. Ó(t) = —2f2
15. Ó(´) = 1 (t - 1)e2f 16. Ó(¥) = -^(2t - 1)e-f
17. Ó(x) = ix2(lnx)3 18. Ó(x) = -2x1/2 cosx
7 xef - tex 2 .
19. Ó(x) = J (1 — t)2et g(t) dt 20. Ó(x) = x-1/2J t-3/2sin(x - t)g(t) dt
23. (b) y = y0cos t + yd sin t + / sin(f — s)g(s) ds
Previous << 1 .. 371 372 373 374 375 376 < 377 > 378 379 380 381 382 383 .. 609 >> Next