Example B Consider the two linearly independent functions (1) (2) Y = 1, y = 3k. A second-order equation having these solutions is (4.96) 3k 1 3k+1 1 3k+2 Ук 1 1 1 3k Yk+1 Yk 1 Yk+1 3 0, (4.97) Yk+2 Yk+2 1 9. or Yk+2 – 4yk+1 +3yk 0. (4.98)
Example B Consider the two linearly independent functions (1) (2) Y = 1, y = 3k. A second-order equation having these solutions is (4.96) 3k 1 3k+1 1 3k+2 Ук 1 1 1 3k Yk+1 Yk 1 Yk+1 3 0, (4.97) Yk+2 Yk+2 1 9. or Yk+2 – 4yk+1 +3yk 0. (4.98)
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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Explain the determine

Transcribed Image Text:Example B
Consider the two linearly independent functions
(2) – 3k.
Y = 1, Yk
(1)
(4.96)
A second-order equation having these solutions is
3k
1 3k+1
3k+2
Yk
1
Ук
1
1
Yk+1
3k
Yk+1
1
3
= 0,
(4.97)
Yk+2
1
Yk+2
1
or
Ук+2 — 4ук+1 + 3уk
= 0.
(4.98)
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