(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2xy" + y' + xy =0 xo=0

find the indicial equation, recurrence relation and series solution.

2. Relevant equations

3. The attempt at a solution

I've done most of the work but i don't know how to use a recurrence relation to obtain a y1 and y2 series solution.

this is what i've done:

xy= sum (n=2 to infinity) an-2 x^(r+n-1)

y'= sum(n=1 to infinity) (r+n) an x^(r+n-1)

2xy''= 2*sum (n=2 to infinity) (r+n) (r+n-1) an x^(r+n-1)

indicial equation:

rao + 2r(r-1) ao=0

r+ 2r^2-2 = 0

r= 0 , r=1/2

{(r+n) (r+n-1) an + (r+n) an + an-2}=0

an= - an-2/ (r+n)(r+n-1)

r=0:

ao=1 a1=0

a2= a0/2*1

a3= a1/ 3*2

a4= a2/4*3

a5= a3/5*4

what kind of pattern could i get out of this? the denominator looks like an n! but not exactly. Where can i go from here to get a y1 ?

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# Homework Help: Find general solution from recurrence relation, done most of work

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