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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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(a) 1.61263, 2.48097, 3.74556, 5.49595
(b) 1.61263, 2.48292, 3.74552, 5.49589
1.26224, 1.42962 1.26272, 1.42999
(a) -1.44768, -2.144478,
(b) -1.44765, -2.143692,
(a) 0.590897, 0.799950,
(b) 2.592926, 2.799988, +1 = (38h3/3) exp(4tn) +1 = (2h3/3) exp(2tn), en+1 = (4h3/3) exp(2tn), h = 2.271
h = 2.281
1.19512, 1.38122, 1.55929 1.22526, 1.42273, 1.65511
1.16653, 1.74969 1.16663, 1.74992
|en+11 < 37, 758.8h3 on 2 < t < 2 |en+1| < 4.92624h3 on 2 < t < 1,
|en+11 < 9.85227h3 on 2 < t < 1 19. h = 2.223 21. h = 2.117 1.72956 24. 1.62268, 1.33435,
1.92572 26. 1.12485, 1.21886,
|e1| < 2.22193389 |e11 < 2.222814269 |e1| < 2.22162854
1.12789,
1.34149,
0.995130
1.47264
Section
1. (a)
(b)
2. (a)
(b)
3. (a)
(b)
4. (a)
(b)
5. (a)
(b)
6. (a)
(b)
7. (a)
(b)
8. (a)
(b)
9. (a)
(b)
12. (a)
(b)
11. (a)
(b)
12. (a)
(b)
.19516,
.19516,
.62231,
.62230,
.20535,
.20535,
.12484,
.12484,
1.512172,
1.522169,
1.38127, 1.38127 1.33362, 1.33362 1.42295, 1.42296 1.21884, 1.21884
2.524138
2.524138
1.55918
1.55918 1.12686 1.12685
1.65553
1.65553
1.34147
1.34147
2.542125
2.542125
1.72968
1.72968 2.993839 2.993826
1.92638
1.92638
1.47262
1.47262
2.564286
2.564286
-2.924517, -2.864125, -2.816377, -2.779726 -2.924517, -2.864125, -2.816377, -2.779726
.96825,
.96828,
.925725
1.925711
.96219,
1.96219,
.61262,
.61262,
7.
7.88924, 1.28516 1.28515
5.12892,
5.12892,
2.48291,
2.48291,
1.44764, -2.143543.
1.44764, -2.143427
22.8349, 22.8355,
2.42862
2.42862
6.43139,
6.43139,
3.74548,
3.74548, 1.26289 1.26295
55.5957
55.5982
4.12352
4.12352
7.92338
7.92338
5.49587
5.49587 1.41228 1.41211
.592929,
.592929,
2.822222,
2.822222,
1.166667,
1.166667,
1.75222
1.75222
718
Answers to Problems
See SSM for detailed solutions to 4a
4bc, 7a 7bc
16
2ab 2c, 4ab
4cd, 5ac
2ab
Section 8.4, page 444
3.
9.
10.
11.
12.
(a) 1
(b) 1 (c) 1
(a) 1
(b) 1 (c) 1
(a) 0
(b) 0 (c) 0
(a) 2
(b) 2 (c) 2
(a) 0
(b) 0 (c) 0
(a) 3
(b) 3
(c) 3
(a) 1
(b) 1 (c) 1
(a) -
(b) -(c) -
(a) 0
(b) 0 (c) 0
7296801
7296802 7296805 906382, 906391, 906395, 56428577
1.8934697
1.8934698 1.8934711
2.179567 2.179582 2.179611 0.59090918
2.
4.
6.
(a) 0
(b) 0 (c) 0
(a) 1
(b) 1 (c) 1
(a) -
(b) -(c) -
56428581, 0.59090923 56428588, 0.59090952
96828, 7.88907, 20.8356, 55.5984
96829, 7.88909, 20.8357, 55.5986 96831, 7.88926, 20.8364, 55.6015 9257133, 1.285148, 2.408595, 4.103495 9257124, 1.285148, 2.408595, 4.103495 9257248, 1.285158, 2.408594, 4.103493 962186, 5.108903, 6.431390, 7.923385 962186, 5.108903, 6.431390, 7.923385 962186, 5.108903, 6.431390, 7.923385 612622, 2.480909, 3.745479, 5.495872
612622, 2.480909, 3.745479, 5.495873
612623, 2.480905, 3.745473, 5.495869 1.447639, -0.1436281, 1.060946, 1.410122 1.447638, -0.1436762, 1.060913, 1.410103 1.447621, -0.1447219, 1.060717, 1.410027 5909091, 0.8000000, 1.166667, 1.750000
5909091, 0.8000000, 1.166667, 1.750000
5909092, 0.8000002, 1.166667, 1.750001
993852,
993846,
993869,
4726173,
4726189,
4726199,
0.779693
0.779692
0.779680
0.925764 0.925746 0.925837 1.6126215 1.6126231 1.6126256 , -0.753135 , -0.753137 , 0.753089
Section 8.5, page 454
(b) () - 1(t) = 0.001 et
1.
2.
3.
4.
5.
^as t
(b) () = ln[ '/(2 - el)]; 2() = ln[1/(1 - t)]
(a,b) h = 0.00025 is sufficient. (c) h = 0.005 is sufficient.
(a) y = 4e-10t + (t2/4) (c) Runge-Kutta is stable for h = 0.25 but unstable
for h = 0.3. (d) h = 5/13 = 0.384615 is small enough.
(a) y = t 6. (a) y = t2
Section 8.6, page 457
1. (a) 1.26, 0.76; 1.7714,1.4824; 2.58991,2.3703; 3.82374,3.60413;
5.64246, 5.38885
(b) 1.32493, 0.758933; 1.93679, 1.57919; 2.93414, 2.66099; 4.48318, 4.22639;
6.84236, 6.56452
(c) 1.32489, 0.759516; 1.9369,1.57999; 2.93459,2.66201; 4.48422,4.22784;
6.8444, 6.56684
2. (a) 1.451, 1.232; 2.16133,1.65988; 3.29292,2.55559; 5.16361,4.7916;
8.54951, 12.0464
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