mateomy
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(Working out of Boas chapter 12, section 11)
<br /> 3xy'' + (3x + 1)y' + y = 0<br />
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
<br /> y = \sum_{n=0}^{\infty} c_n x^{n+s}<br />
*I know in a normal expansion it's simpy x^n but from my understanding we're to multiply the summation by another factor of x^s, or whatever variable we choose.
...doing like wise for the respective derivatives:
<br /> y' = \sum_{n=0}^{\infty} c_n (n+s) x^{n+s-1}<br />
<br /> y'' = \sum_{n=0}^{\infty} c_n (n+s-1) (n+s) x^{n+s-2}<br />
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.
<br /> 3xy'' + (3x + 1)y' + y = 0<br />
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
<br /> y = \sum_{n=0}^{\infty} c_n x^{n+s}<br />
*I know in a normal expansion it's simpy x^n but from my understanding we're to multiply the summation by another factor of x^s, or whatever variable we choose.
...doing like wise for the respective derivatives:
<br /> y' = \sum_{n=0}^{\infty} c_n (n+s) x^{n+s-1}<br />
<br /> y'' = \sum_{n=0}^{\infty} c_n (n+s-1) (n+s) x^{n+s-2}<br />
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.