Уk+1 (1, 1) Ук FIGURE 2.11: y+1 = Yk. k+1 Plot the following curves, locate any fixed points, and obtain asymp- totic expansions to their solution as k (a) Yk+1 = y + a², real number, a = Yk (v; +3) 3y+1 (b) Yk+1 = (c) 2y%+1 - 5yk+1Yk + 2y% = 2, (d) Yk+1 ayk+1 Yk+a > 5y%-6yk+2 6y-8yk+3' 5y+6yk+19 Y+5 (e) Yk+1 (f) 5yk+1 k+1 = Yk + 6.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
Plot the following curves, locate any fixed points, and obtain asymp-
totic expansions to their solution as k
(a) Yk+1 = y + a²,
real number,
a =
Yk (v; +3)
3y+1
(b) Yk+1 =
(c) 2y%+1 - 5yk+1Yk + 2y% = 2,
(d) Yk+1
ayk+1
Yk+a >
5y%-6yk+2
6y-8yk+3'
5y+6yk+19
Y+5
(e) Yk+1
(f) 5yk+1
k+1
= Yk + 6.
Transcribed Image Text:Plot the following curves, locate any fixed points, and obtain asymp- totic expansions to their solution as k (a) Yk+1 = y + a², real number, a = Yk (v; +3) 3y+1 (b) Yk+1 = (c) 2y%+1 - 5yk+1Yk + 2y% = 2, (d) Yk+1 ayk+1 Yk+a > 5y%-6yk+2 6y-8yk+3' 5y+6yk+19 Y+5 (e) Yk+1 (f) 5yk+1 k+1 = Yk + 6.
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