
#1
Dec1912, 12:44 PM

P: 192

Why sometimes we search solution of power series in the way:
[tex]y(x)=\sum^{\infty}_{n=0}a_nx^n[/tex] and sometimes [tex]y(x)=\sum^{\infty}_{n=0}a_nx^{n+1}[/tex]??? 



#2
Dec2012, 05:44 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

hi matematikuvol!
sometimes one gives neater equations than the other … they'll both work (provided, of course, that y(0) = 0) 



#3
Dec2112, 01:22 AM

P: 192

I think that in the case when
[tex]\alpha(x)y''(x)+\beta(x)y'(x)+\gamma(x)y(x)=0[/tex] if ##\alpha(0)=0## you must work with ##\sum^{\infty}_{n=0}a_nx^{n+k}##, but I'm not sure. 


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