Can you substitute equation 28 into equation 27 and try to achieve equation 30? Please I need it today
Can you substitute equation 28 into equation 27 and try to achieve equation 30? Please I need it today
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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Question
Can you substitute equation 28 into equation 27 and try to achieve equation 30?
Please I need it today
![L-1(2)= ¿L_¡(2)+1+Lo(2)
(27)
Because the Y,(1) are easy to calculate [Y,(1)=1 for all p], one
immediately concludes from (26) that the general solution of (26) is
L, = A,(à)
(1– (1– 42)/2\p+1
(1+ (1– 42)/2\+1
+ A2(2) |
|
|
(28)
The problem now is to determine the constants A(2) and A2(i).
From the definition (25), it is clear that for any p the first term in the sum
L,(2) is proportional to iP+'. This is compatible with the result (28)
only if
A2(2) =0
(29)
The expression of A,(2) is then easy to find from the boundary condition
(27) and one ends up with
(1-(1-42)2\p+3 1
L,(4) =|
(30)
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F449fe0b2-a310-4385-aa4a-fe9b6697a61a%2Fd2beda64-c931-4f82-b6f6-36a033dd2324%2Fn9sha0c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:L-1(2)= ¿L_¡(2)+1+Lo(2)
(27)
Because the Y,(1) are easy to calculate [Y,(1)=1 for all p], one
immediately concludes from (26) that the general solution of (26) is
L, = A,(à)
(1– (1– 42)/2\p+1
(1+ (1– 42)/2\+1
+ A2(2) |
|
|
(28)
The problem now is to determine the constants A(2) and A2(i).
From the definition (25), it is clear that for any p the first term in the sum
L,(2) is proportional to iP+'. This is compatible with the result (28)
only if
A2(2) =0
(29)
The expression of A,(2) is then easy to find from the boundary condition
(27) and one ends up with
(1-(1-42)2\p+3 1
L,(4) =|
(30)
2
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