6.6.1 Example A The nonlinear equation 2(k +1,1) = [z(k, l+1)]", (6.140) where is a constant, can be transformed to the linear equation (w(k +1,1) = yw(k,l+1) (6.141) by means of the substitution w(k, l) = log z(k, l). (6.142) %3D Equation (6.141) has the solution w(k, l) = y* f(k + 1), (6.143) where f is an arbitrary function of (k +1). Therefore, equation (6.140) has the solution 2(k, l) = exp[w(k, l)] = exp{7* f (k +1)]. (6.144)
6.6.1 Example A The nonlinear equation 2(k +1,1) = [z(k, l+1)]", (6.140) where is a constant, can be transformed to the linear equation (w(k +1,1) = yw(k,l+1) (6.141) by means of the substitution w(k, l) = log z(k, l). (6.142) %3D Equation (6.141) has the solution w(k, l) = y* f(k + 1), (6.143) where f is an arbitrary function of (k +1). Therefore, equation (6.140) has the solution 2(k, l) = exp[w(k, l)] = exp{7* f (k +1)]. (6.144)
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 yellow
![6.6.1
Example A
The nonlinear equation
z(k+1,l) = [z(k, l+1)]",
(6.140)
where y is a constant, can be transformed to the linear equation
w(k +1,1) = yw(k,l+1)
(6.141)
by means of the substitution
w(k, l) = log z(k, 1).
(6.142)
Equation (6.141) has the solution
w(k,l) = y* f(k +1),
(6.143)
where f is an arbitrary function of (k + l). Therefore, equation (6.140) has
the solution
z(k, 1) = exp{w(k, 1)] = exp[y* f(k + 1)].
(6.144)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9c08ba6-0357-493f-88a3-1c046e8fa0d2%2F4be722f9-e1a1-43d2-9285-015dba8c9147%2Fqtcymlk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.6.1
Example A
The nonlinear equation
z(k+1,l) = [z(k, l+1)]",
(6.140)
where y is a constant, can be transformed to the linear equation
w(k +1,1) = yw(k,l+1)
(6.141)
by means of the substitution
w(k, l) = log z(k, 1).
(6.142)
Equation (6.141) has the solution
w(k,l) = y* f(k +1),
(6.143)
where f is an arbitrary function of (k + l). Therefore, equation (6.140) has
the solution
z(k, 1) = exp{w(k, 1)] = exp[y* f(k + 1)].
(6.144)
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