Frobenius Method on higher degrees

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I would like to know if the Frobenius Method works on higher degree ODEs (3rd and so on). I tried to search some literature, articles etc on this matter, however I could not find anything except this: Using Frobenius method .

The article linked on that question says we can generalize it for higher degree ODEs. But I am usure about the results achieved by the authors. The thing is: the article does not seem to be very formal, rigorous. So I would like to know your thoughts on this matter.

Can we use the method on higher degrees ODEs? Do you know any article on this matter?

Thanks