Method Of Frobenius: 4xy'' + 2y' + y = 0

rooney

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Feb 9, 2008
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4xy''+2y'+y=0

i found r1 = 0 and r2 = 1/2
for r=0 i found the recurrence relation to be:

C(sub n) = -C(sub n-1)/(2n(2n-1))

with C(sub n) and C(sub n-1) meaning C with the subscripts n and n-1 (respectively).

I need help with the next part, which is plugging in values of "n" to find a general form for odd numbers and even numbers. I've tried doing both, but I can't find a pattern. Please let me know if I need to explain more thoroughly. Thank you.
 
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