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 7th edition - Boyce W.E

Boyce W.E Elementary differential equations 7th edition - Wiley publishing , 2001. - 1310 p.
ISBN 0-471-31999-6
Download (direct link): elementarydifferentialequat2001.pdf
Previous << 1 .. 296 297 298 299 300 301 < 302 > 303 304 305 306 307 308 .. 486 >> Next

-f
y — c1 cos t I c2 sin i I f (°3 cos 2
y — c1et + c2e-t + c3e2t + c4e
2tef + c3t2et I c4f I c5
y — c1 + c2f + c3ef + c4e-t + c5 cos f + c6 sin f
f 2f
y — c1 + c2e + c3^ + c4 cos f + c5 sin f y — c1 + c2e2t + e-t (c3 cos \/3 f + c4 sin \/3 f)
y — ef[(c1 + c2f) cos f + (c3 + c4f) sin f] + e-t[(c5 + c6f) cos f + (c7 + c8f) sin f]
22. y — (c1 + c2f) cos f + (c3 + c4t) sin f 23. y — c1et + c2e'
24. y — c1e-t + c2e(-2+F2)t + c3e(-2-'^2)t
25. y — c1e-t/2 + c2e-t/3cos(f/V3) + c3e-t/3 sin(f/V3)
26. y — cje3t + c2e-2t + c3e(3+e3)t + c4e(3-e3)t
,(2^V5)t + (2-V5)f
u
6
e
694
Answers to Problems
See SSM for detailed solutions to 27 ,29 ,30, 31
34, 37, 38a, 39ac 1
5, 9, 13
17, 20, 22a 22be
1, 4, 5, 7
27. y = c1e t/2 + c2e t/4 + c3e 1 cos2t + c4e 1 sin2t
28. y = c1 e-t cos t + c2e-t sin t + c3e—2t cos(\/3 t) + c4e—2t sin(\/3 t)
29. y = 2 — 2cost + sint
30. y = 2 e—t/v^ sin (t/v'?) — 2et/v^sin(t/V?)
31. y = 2t — 3 32. y = 2cost — sin t
33. y =— 3el — 110e2t — 6e—2t — if e—1/2 34. y = 123e—t + ff et/2cos t + j3
35. y = 8 — 18e—1/3 + 8e—1/2
36. y = 23 e— t cos t — if e—t sin t — 13e—2t cos(V3t) + e—2t sin(V3 0
37. y = 2 (cosh t — cos t) + 2 (sinh t — sin t)
38. (a) W = c, a constant (b) W =—8 (c) W = 4
39. (b) u1 = c1 cos t + c2 sin t + c3 cosV6 f + c4 sin-/6 t
Section 4.3, page 224
1. y = c1et + c2tet + c3e—t + 1 te—t + 3
2. y = c1 et + c2e— t + c3 cos t + c4 sin t — 3t — 4 t sin t
3. y = c1e— t + c2 cos t + c3 sin t + i te—t + 4(t — 1)
4. y = c1 + c2et + c3e—t + cos t
5. y = c1 + c2t + c3e—2t + c4e2t — 1 et — 48t4 — ^t2
6. y = c1 cos t + c2 sin f + c3t cos t + c4t sin t + 3 + 9 cos2t
7. y = c1 + c2t + c3t2 + c4e—t + et/2[cf cos(v/3 t/2) + c6 sin^V^ t/2)] + 23t4
8. y = c1 + c2t + c3t2 + c4e— t + 2O sin2t + 410 cos2t
9. y = 13(1 — cos2t) + 1t2
10. y = (t — 4) cos t — (2t + 4) sin t + 3t + 4
11. y = 1 + 1 (t2 + 3t) — tet
12. y =—f cos t — f sin t + 25e—t + ijOet + 520e—3t + 6f cos2t — j490 sin2t
13. 7 (t) = t ( A0t3 + A1t2 + A2t + A3) + Bt2et
14. Y (t) = t ( A0t + A1)e—t + B cos t + C sin t
15. Y (t) = At2et + Bcos t + C sin t
16. Y (t) = At2 + ( B0t + B1)et + t (C cos2t + D sin2t)
17. Y (t) = t ( A0t2 + A1t + A2) + ( B0t + B1) cos t + (C0t + C1) sin t
18. Y(t) = Aet + (B0t + B1)e—t + te— ((Ccos t + D sin t)
19. *0 = kn = ^0an + a an 1 + ••• + an—1a + an
Section 4.4, page 229
1. y = c1 + c2 cos t + c3 sin t — ln cos t — (sin t) ln(sec t + tan t)
2. y = c1 + c2e‘ + c3e— ‘ — 212
3. y = c1et + c2e— 1 + c3e2t + 30e4t
4. y = c1 + c2 cos t + c3 sin t + ln(sec t + tan t) — t cos t + (sin t) ln cos t
5. y = c1et + c2 cos t + c3 sin t — 1 e— ( cos t
6. y = c1 cos t + c2 sin f + c31 cos t + c41 sin t — 112 sin t
7. y = c1 et + c2 cos t + c3 sin t — 2 (cos t) ln cos t + 1 (sin t) ln cos t — 2 t cos t —
+ 2 e\ft (e—s/ cos ds
et/2 sin t
2 t sin t
Answers to Problems
695
See SSM for detailed solutions to 11, 14
16
8. y = Cj + c2el + c3e 1 — lnsin t + ln(cos t + 1) + 2el ? ^e s/ sins^ ds
+ I e—t ? ^es/ sin s^ ds
9. Cj = 0, c2 = 2, c3 = 1 in answer to Problem 4
10. cj = 2, c2 = 7, c3 = —7, c4 = I in answer to Problem 6
11. cj = |, c2 = 2, c3 = —5, t0 = 0 in answer to Problem 7
12. c1 = 3, c2 = 0, c3 = —en/2, t0 = n/2 in answer to Problem 8
13. Y (x) = x4/15
14. Y(t) = 1 f [et—s — sin(t — s) — cos(t — s)]er(s) ds
Jt0
15. Y (t) = if [sinh(t — s) — sin(t — s)]er(s) ds
Jt0
16. Y(t) = i f e(t—s')(t — s)2er(s) ds; Y(t) = —tel ln |t|
2 Jt0
17. Y (x) = if X [(x/t2) — 2(x2/t3) + (x3/t4)]g(t) dt
2 J xn
CHAPTER 5 Section 5.1, page 237
2, 5, 9, 12, 13
18, 19, 23, 25, 28
1. p = 1
3. p = to
5. p = 2
7. p = 3
^ (- 1)nx2n+1
9. >-----------------------------------------, p = oo
(2n + 1)!
11. 1 + (x - 1), p = to
V+ (x - 1)n, n
13. (-1)n
p =1
15. ? xn, p = 1
n=o
2. p = 2
4. p = 2
6. p = 1
8. p = e xn
1oi:
n=o
n!
p = to
12. 1 - 2(x + 1) + (x + 1)2, p = to
to
14. (-1)nxn, p = 1
n=o
TO
16. (-1)n+1(x - 2)n, p = 1
n=o
17. / = 1 + 22x-
+ (n + 1)2 xn + •
/ = 22 + 32 • 2x + 42 • 3x2 + 52 • 4x3 + ••• + (n + 2)2(n + 1)xn + •••
18. / = a1 + 2a2x + 3a3x + 4a4^ + ••• + (n + 1)an+1 x + •••
TOTO
= 1] nanxn-1 = 1](n + 1)a
n+1
xn
n= 1
n=o
y = 2a2 + 6a3 x + 12a4 x2 + 2oa5 x3 + ••• + (n + 2)(n + 1)an+2 xn + •••
TOTO
= n(n - 1)anxn-2 = (n + 2)(n + 1)an+2xn
21. ^2(n+2)(n+1)an+2 xn n=o 22
23. TO !> + 1)anxn n=o 24
25. TO J2 [(n + 2)(n + 1)an+2 + nan]xn n=o 26
27. TO J2[(n + 1)nan+1 + an]xn 28
an-1J
n= 1
n = 1, 2,...;
n=o
a
2
aoe
o
n
696
Answers to Problems
See SSM for detailed solutions to 2
3
Section 5.2, page 247
1 3n+2 = 3n/(n + 2)(n + 1)
x2 x4 x6
7l(x) = 1 + — + — + — + •
2!
x3
4!
x5
6!
=
x2n
= coshx
y2(x) = x +-------\------\ + •
J2 3! 5! 7!
2 an+2 = an/(n + 2)
x2 x4 x6
yi (x) = 1 +------+-----------------------------+-
^ 2 2 • 4 2 • 4 • 6
x3 x5 x7
y2(x) = x +-------\---------------------\--------------------
J2 3 3 ? 5 3-5-7
n=0 (2n)!
to x2 n+1
= 'y------------------- = sinh x
n=0 (2n + 1)!
\
\
=
n=0
to
Previous << 1 .. 296 297 298 299 300 301 < 302 > 303 304 305 306 307 308 .. 486 >> Next