Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" - 2xy n-constant Any saluhion tuis equation is° called k = ncnt2). Ligendre's function. Let %3D 8.1. Subetitute Eamx in Legendre's equation & aive at S-2 S-0 Q.2 Find a generul formula lby equating x, 'x' & x"!, n>2 celticients aqhal to zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains onlyodd powers x series solutron is the cohene while
Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" - 2xy n-constant Any saluhion tuis equation is° called k = ncnt2). Ligendre's function. Let %3D 8.1. Subetitute Eamx in Legendre's equation & aive at S-2 S-0 Q.2 Find a generul formula lby equating x, 'x' & x"!, n>2 celticients aqhal to zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains onlyodd powers x series solutron is the cohene while
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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Solve only q3
Transcribed Image Text:Any saluhion d this' equation is" called
Considir the
Legendre's clifterential equation
(1-x²) Y" - 2xy
Any saluhion tis equation is" called
gendre's function.
8.1.
n-constant
Let
Eamx in
equation & arive at
k = ncnt2).
Legendr's
%3D
Substitute
|
S-2
S-0
Q.2
Find a generel formula for as
y equating x
ceticients qual to
x 'x' & x", na2
zero.
Show that
fom
yex)=DQ0Y,(x) + a, y,(x)
y,cx) contains only even powers ofx
,cx) Contains only-odd powers x
series
sl utron
is
the
cohene
while
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