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 .. 369 370 371 372 373 374 < 375 > 376 377 378 379 380 381 .. 609 >> Next

25c, 27, 28, 30, 34
39, 40, 43
2, 4, 8
12, 14, 15, 18, 21
25, 27, 30, 32, 34, 36
37
2, 6, 7, 12, 15
23.
24.
25.
26.
27.
28.
30.
y ^ 0 for a < 0; y becomes unbounded for a > 1
y ^ 0 for a < 1; there is no a for which all nonzero solutions become unbounded.
(a) y = 1 (1 + 2p)e-2t + 5 (4 - 2p)et/2
(b) y = 0.71548 when t = 5 ln6 = 0.71670 (c) = 2
(a) y = (6 + e)e-2t - (4 + e)e-3t
(b) tm = ln[(12 + 3)/(12 + 2)], = 27(6 + )3/(4 + )2
(c) = 6(1 + V3) = 16.3923 (d) tm ^ ln(3/2),
+ 3y + 2y = 0 is one such equation.

= , t 1 + a, + ln t
29. y = 1 ln t + c2 + t
31. y
y
y = (1/k) ln l(k - t)/(k + t)| + c2 if c1 = k2 > 0; y = (2/k) arctan(t/k) + c2 if c1 = k2 < 0; y = 2t-1 + c2 if c1 = 0; also y = y =3 (t - 2q)y t + c1 + c2; also y =
factor.
Hint: ji(v) = v 3 is an integrating
32.
33.
34. 36. 38. 40.
42.
43.
y = c1 e- t + c2 - te- t y = c11 - ln 11 + c111 + c2 if c1 = 0; y2 = c1 t + c2
3y3 - 2c1 y + c2 = 2t; also y = c
yln |y| - y + c1 y + t = c2;also y = c y = 4 (t+1)3/2- 3 y = 3ln t - 2 ln(t2 + 1) - 5 arctan t + 2 + |ln2 + 5n
y = 112 + 3
y = 212 + c2 if c1 = 0; also y = c 35. y = c1 sin(t + c2) = k1 sin t + k2 cos t 37. t + c2 = (y 2c1)(y + c1)1/2 39. ey = ( t + c2 ) 2 + c1 41. y = 2(1 - t)-2
Section 3.2, page 145
1. 2/ 2. 1
te
MO
1
3. e-4t 4. x2 ex
5. -e21 6. 0
7. 0 < t < 8. - < t < 1
9. 0 < t < 4 10. 0 < t <
11. 0 < x < 3 12. 2 < x < 2/
3
14. The equation is nonlinear. 15. The equation is nonhomogeneous.
16. No 17. 3te2t + ce2t
18. tet + ct 19. 5W (f, g)
20. -4(f cos t - sin t)
21. y() = 3 e-2t + 2 et, y2(t) = - 1 e-2t + 3 e
22. t- 1) + 2 e-(t-1), yt(2 = -2e -3(t-1) + 1 e-(t-1)
3( 2
-
e
'---'l(N
-
II
y1
23. Yes 24. Yes
25. Yes x2/2 26. Yes
28. Yes, y = c1 e-x2/2 fX et2/2 dt + c2e-
29. No 0
30. 1 l(f) j(x) = exp f ( 1 cos x\
Yes, y = - c1 dt + c2 -j + X Jdx.
l(x) _ Jx0 1
31. Yes, y = c1 x-1 + c2x 33. x2/" + 3xj' + (1 + x2 - v2)i =
34. (1 - x2)l - 2xj + a(a + 1)i =0 35. 1 --- x = 0
37. The Legendre and Airy equations are self-adjoint.
Section 3.3, page 152
1. Independent 2. Dependent
3. Independent 4. Dependent
5. Dependent 6. Independent
7. Independent if origin is interior to interval; otherwise dependent
Answers to Problems
689
See SSM for detailed solutions to 20, 24, 26, 27
28
1, 5, 7
11, 14, 18, 22, 23a
23b, 25abcd, 31, 33
35, 38, 39
1,9, 12
8. Independent if origin is interior to interval; otherwise dependent
9. Independent; W is not always zero 10. Independent; W is not always zero
11. W(c171, c272) = c1c2 W(71, 72) = 0 12. W( 74) = ---2 W(71, 72)
Previous << 1 .. 369 370 371 372 373 374 < 375 > 376 377 378 379 380 381 .. 609 >> Next