6.3.1 Example A Consider Yk+1Yk + ayk+1+byk 0, (6.28) where a, b, and c are constants. With x = 1/yk, we obtain bæk+1 + axk +1=0, (6.29) which is a first-order linear inhomogeneous equation with constant coefficients. This equation has the solution a k Xk ミD if a + -b, (6.30) a + b Xk = D - -k, if a = -b, (6.31) where D is an arbitrary constant. The substitution of either of these results into yk = 1/xk gives the general solution to equation (6.28).
6.3.1 Example A Consider Yk+1Yk + ayk+1+byk 0, (6.28) where a, b, and c are constants. With x = 1/yk, we obtain bæk+1 + axk +1=0, (6.29) which is a first-order linear inhomogeneous equation with constant coefficients. This equation has the solution a k Xk ミD if a + -b, (6.30) a + b Xk = D - -k, if a = -b, (6.31) where D is an arbitrary constant. The substitution of either of these results into yk = 1/xk gives the general solution to equation (6.28).
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 blue
Transcribed Image Text:6.3.1
Example A
Consider
Yk+1Yk + aYk+1+byk = 0,
(6.28)
where a, b, and c are constants. With xk = 1/yk, we obtain
bx+1 + ax +1=0,
(6.29)
which is a first-order linear inhomogeneous equation with constant coefficients.
This equation has the solution
=D(-)*
а
k
1
Xk = D
if a + -b,
(6.30)
a + b'
1
-k,
if a = -b,
(6.31)
b
where D is an arbitrary constant. The substitution of either of these results
into yk = 1/xk gives the general solution to equation (6.28).
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