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
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Chapter2: Second-order Linear Odes
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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.
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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