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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Уk+1
(1, 1)
Ук
FIGURE 2.11: y+1 = Yk.
k+1
Transcribed Image Text:Уk+1 (1, 1) Ук FIGURE 2.11: y+1 = Yk. k+1
2.21. Plot the following curves, locate any fixed points, and obtain asymp-
totic expansions to their solution as k
(а) Ук+1 —
yi + a?,
a = real number,
(b) Ук+1
Yr (y% +3)
3y?+1,
(c) 2y%+1- 5yk+1Yk + 2y% = 2,
(d) Yk+1
ayk+1
Yk+a »
5y-6yk+2
6y -8yk+3'
(е) Ук+1 —
5y+6yk+19
(f) 5ук+1
(8) บ+1
Yk + 6.
Transcribed Image Text:2.21. Plot the following curves, locate any fixed points, and obtain asymp- totic expansions to their solution as k (а) Ук+1 — yi + a?, a = real number, (b) Ук+1 Yr (y% +3) 3y?+1, (c) 2y%+1- 5yk+1Yk + 2y% = 2, (d) Yk+1 ayk+1 Yk+a » 5y-6yk+2 6y -8yk+3' (е) Ук+1 — 5y+6yk+19 (f) 5ук+1 (8) บ+1 Yk + 6.
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