Page 853 - Advanced_Engineering_Mathematics o'neil
P. 853
Answers to Selected Problems 833
10
2
8
–1.5 –1 –0.5 0 0.5
6
0
y
–2 4
2
–4
0
–6 8 12 16 20 24
x
FIGURE A.15 Phase portrait for Problem
FIGURE A.16 Phase portrait for Problem
9, Section 10.6.
13(a), Section 10.6.
10
8
6
y
4
2
0
0 10 20 30 40 50 60 70
x
FIGURE A.17 Phase portrait for Problem
13(c), Section 10.6.
√
9. −2 ± 3i, spiral point. The solution is
√ √
−2t −2t
c 1 e cos( 3t) − c 2 e sin( 3t)
X = √ √
c 1 e −2t sin( 3t) + 3c 2 e −2t cos( 3t)
Figure A.15 is a phase portrait.
11.
x = ax 1 − bx 1 x 2 − Hx 1 , x =−kx 2 + cx 1 x 2 − Hx 2
1 2
13. Figure A.16 is a phase portrait for (a), and Figure A.17 for (c).
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
October 14, 2010 17:50 THM/NEIL Page-833 27410_25_Ans_p801-866
