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[tex]

3xy'' + (3x + 1)y' + y = 0

[/tex]

I'm asked to solve the differential equation using the method of Frobenius but I'm finding the way Boas introduces/explains/exemplifies the method to be incredibly confusing. So, I used some google-fu and was even more confused. Seems like everyone has a different plan of attack for these problems.

What I've done so far is to assume

[tex]

y = \sum_{n=0}^{\infty} c_n x^{n+s}

[/tex]

*I know in a normal expansion it's simpy [itex]x^n[/itex] but from my understanding we're to multiply the summation by another factor of [itex]x^s[/itex], or whatever variable we choose.

...doing like wise for the respective derivatives:

[tex]

y' = \sum_{n=0}^{\infty} c_n (n+s) x^{n+s-1}

[/tex]

[tex]

y'' = \sum_{n=0}^{\infty} c_n (n+s-1) (n+s) x^{n+s-2}

[/tex]

then we substitute these expansions into the respective places within the original equation.

Now this is where I'm getting REALLY REALLY confused. Boas says to make a table and then from there find the indicial equation. From various pdf's and youtube videos I'm getting different information. Can anyone please point me onto the right path?

Thanks.