4. Using the substitution x = cos 0, show that the following differential equation d?y dy sin 0 ·+ cos 0 + [n(n+ 1) sin 8]y = 0 de? de can be transformed into the Legendre's equation. Show the complete details.
4. Using the substitution x = cos 0, show that the following differential equation d?y dy sin 0 ·+ cos 0 + [n(n+ 1) sin 8]y = 0 de? de can be transformed into the Legendre's equation. Show the complete details.
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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Write complete solution. Write legibly.
![4. Using the substitution x = cos 0, show that the following differential equation
d?y
dy
sin 0
·+ cos 0
+ [n(n+ 1) sin 8]y = 0
de?
de
can be transformed into the Legendre's equation. Show the complete details.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f581fda-cf7b-4d40-81f5-1802eaab5516%2Fcd1914de-50f8-474b-96c7-88d5674ce993%2Fgg3blnt_processed.png&w=3840&q=75)
Transcribed Image Text:4. Using the substitution x = cos 0, show that the following differential equation
d?y
dy
sin 0
·+ cos 0
+ [n(n+ 1) sin 8]y = 0
de?
de
can be transformed into the Legendre's equation. Show the complete details.
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