2.1. Solve the following difference equations: (a) Yk+1 +Yk = 2+ k, %3D (b) Yk+1 - 2uk = k3.

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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PROBLEMS
Section 2.2
2.1. Solve the following difference equations:
(a) Yk+1+yYk = 2+ k,
= k³,
(b) Yk+1 – 2yk
3kyk = 0,
1/k(k+ 1),
(с) Ук+1 —
(d) Yk+1 – Yk =
(e) Yk+1 + Yk =1/k(k+1),
(f) (k+2)yk+1
- (k + 1)yk = 5+ 2k – k²,
(g) Yk+1+Yk = k + 2 · 3k,
(h) Yk+1 – Yk = ke*,
aa2k yk = Bak,
(J) Yk+1 – ayk = cos(bk),
,2k
(i) Yk+1
(k) Yk+1 + Yk
= (-1)*,
(1)
Yk+1
k+1
-* = k.
Transcribed Image Text:PROBLEMS Section 2.2 2.1. Solve the following difference equations: (a) Yk+1+yYk = 2+ k, = k³, (b) Yk+1 – 2yk 3kyk = 0, 1/k(k+ 1), (с) Ук+1 — (d) Yk+1 – Yk = (e) Yk+1 + Yk =1/k(k+1), (f) (k+2)yk+1 - (k + 1)yk = 5+ 2k – k², (g) Yk+1+Yk = k + 2 · 3k, (h) Yk+1 – Yk = ke*, aa2k yk = Bak, (J) Yk+1 – ayk = cos(bk), ,2k (i) Yk+1 (k) Yk+1 + Yk = (-1)*, (1) Yk+1 k+1 -* = k.
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