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Need quick help with Series, it will only take a few seconds!

by twisted079
Tags: seconds, series
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twisted079
#1
Nov27-12, 07:34 PM
P: 25
So the differential equation I have to solve using power series is
y''-xy=0 when x0 = -1

So i set it up
Ʃ(n+2)(n+1)an+2(x+1)n - x Ʃ an(x+1)n

I know how to generally solve equations like this, but I never solved one like this, where I have to distribute the x ... x(x+1)n ... I just need to figure this part out (I know I left out the n=0 to ∞)
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twisted079
#2
Nov27-12, 08:06 PM
P: 25
Ok I figured it out using a cheap (but valid) math trick... in case anyone is wondering...

xƩan(x+1)n = (x+1-1)Ʃan(x+1)n

Now the x+1 can be distributed to give -Ʃan(x+1)n+1

...anyone care to double check me on this?
Mute
#3
Nov27-12, 08:59 PM
HW Helper
P: 1,391
Quote Quote by twisted079 View Post
Ok I figured it out using a cheap (but valid) math trick... in case anyone is wondering...

xƩan(x+1)n = (x+1-1)Ʃan(x+1)n

Now the x+1 can be distributed to give -Ʃan(x+1)n+1

...anyone care to double check me on this?
Yep, that's the trick you want to use.


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