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Differential Equations Quiz
#9 May
6, 2005
Name____________________ R. Hammack Score
______
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(1) Find find
two linearly independent power series solutions about the ordinary point x=0
of the differential equation y''-2x y'+ y=0.
Try solution y=.
Then y'=n
,
and y''=n(n-1)
Plugging this in:
y''+y'+y=0
n(n-1)-2x
n
+=
0
n(n-1)-
n
+=
0
(k+2)(k+1)-
2k
+=
0
((k+2)(k+1)+(1-2k))=
0
Thus: (k+2)(k+1)+(1-2k)=
0
So =
=
=-
==-
==-
==-
=-
Thus =(1----
... )
=
=
==
==
==
=
Thus =(x++++
... )