Show me the steps of determine green

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Show me the steps of determine green

5.4.1 Example A
The equation
z(k, l) = pz(k+1, l – 1) + (1 – p)z(k – 1, l + 1)
(5.131)
has the sum of its various arguments equal to a constant. Let k +l = m and
define
Uk =
z(k, m – k).
(5.132)
Therefore, equation (5.131) becomes
Vk = pvk+1 + (1– p)vk-1,
(5.133)
which is a second-order ordinary difference equation whose solution is
k
Uk = C1 + C2
(5.134)
Replacing C1 and C2 by arbitrary functions of k+l gives the general solution
to equation (5.131),
k
1 -
z(k, l) = fi(k + l) +
f2(k + l).
(5.135)
Transcribed Image Text:5.4.1 Example A The equation z(k, l) = pz(k+1, l – 1) + (1 – p)z(k – 1, l + 1) (5.131) has the sum of its various arguments equal to a constant. Let k +l = m and define Uk = z(k, m – k). (5.132) Therefore, equation (5.131) becomes Vk = pvk+1 + (1– p)vk-1, (5.133) which is a second-order ordinary difference equation whose solution is k Uk = C1 + C2 (5.134) Replacing C1 and C2 by arbitrary functions of k+l gives the general solution to equation (5.131), k 1 - z(k, l) = fi(k + l) + f2(k + l). (5.135)
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