Letting æk = VYk gives Xk+1 = kxk, (6.88) the solution of which is Cuk = c(k – 1)!. (6.89) Therefore, Yk = [c(k – 1)!]². (6.90) We can obtain this solution to equation (6.87) by a second method. Taking the logarithm of both sides of equation (6.87) gives
Letting æk = VYk gives Xk+1 = kxk, (6.88) the solution of which is Cuk = c(k – 1)!. (6.89) Therefore, Yk = [c(k – 1)!]². (6.90) We can obtain this solution to equation (6.87) by a second method. Taking the logarithm of both sides of equation (6.87) gives
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![6.5.4 Example D
Consider the equation
VYk+1
k/Yk•
(6.87)
Letting xk =
Yk gives
Xk+1
= kak,
(6.88)
the solution of which is
X'k = c(k – 1)!.
(6.89)
Therefore,
[c(k – 1)!]?.
(6.90)
Yk
We can obtain this solution to equation (6.87) by a second method. Taking
the logarithm of both sides of equation (6.87) gives
Zk+1
Zk = log k,
(6.91)
where zk =
1/2(log yk). This last equation is of the form
Zk+1
Pk Zk = Rk
(6.92)
and can be solved
Its solution is
(2* = log[c(k – 1)!],
(6.93)
and, consequently, the result given by equation (6.90) is obtained.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52e77568-6ab0-477a-b8a0-d1d660cfb901%2F0ec7e69d-9e5c-455a-9116-9d32a33bb15d%2Frhvtc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.5.4 Example D
Consider the equation
VYk+1
k/Yk•
(6.87)
Letting xk =
Yk gives
Xk+1
= kak,
(6.88)
the solution of which is
X'k = c(k – 1)!.
(6.89)
Therefore,
[c(k – 1)!]?.
(6.90)
Yk
We can obtain this solution to equation (6.87) by a second method. Taking
the logarithm of both sides of equation (6.87) gives
Zk+1
Zk = log k,
(6.91)
where zk =
1/2(log yk). This last equation is of the form
Zk+1
Pk Zk = Rk
(6.92)
and can be solved
Its solution is
(2* = log[c(k – 1)!],
(6.93)
and, consequently, the result given by equation (6.90) is obtained.
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