- #1
Ratpigeon
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Homework Statement
Find the indicial equation and all power series solutions around 0 of the form
xr Ʃan xn for:
x y'' -(4+x)y'+2y=0
- apparently one of these solutions is a laguerre pilynomial
Homework Equations
the indicial equation is the roots of
r(r-1) +p0r+q0
where p0=lim(x->0)( x(-4-x)/x)=-4
and q0=lim(x->0)( x^2 *2/x)=0
Hence the indicial equation is:
r^2-r - 4r =r(r-5)
The Attempt at a Solution
I have a solution for the root at r=5, but I'm not sure how to do it for r=0, which is the Laguerre one...?
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