(adsbygoogle = window.adsbygoogle || []).push({}); A few problems with the operator method.....

Hey there, I've just started doing the operator method etc in Maths and I was hoping someone could give me a hand here cos I've got a couple of qs (relating to the homework sheet).

http://titus.phy.qub.ac.uk/group/Jorge/AMA203/assignments/ass03_10.pdf [Broken]

In question 1 part 3, with the Hermite equation, I really don't know what to do with it cos it just kinda gets stuck. I multiplied through by x^2 so I could have X^2 D^2 y so I could use the operator (sorry I can't write it up, but if O were the operator, this would look like O(O - 1)). So that part is fine but then that leaves us with x^2 ( 2n + 1 - x^2 )y, and when you've to bring that over to the other side of the eqt, I'm not sure you split it up so you have x^h G(O) y. The others are fine but I don't know about that one because all the powers of x aren't the same and I don't think you can have an x^2 in our G(0). If someone could explain to me where I'm going wrong or where to proceed from here it would be great.

Second of all, and my last question for the moment cos I think the rest of the h/work is ok, do you think there's a specific reason why in question 3 when it asks for the recurrence relation it only gives us one of them? There are 2 values of alpa (0 and 1-b) and what they've given is only applicable for the 0 one. Am I missing the point of something here? Oh, and one other teeny thing, just about when it says find the series solution for around x=0. We don't actually have tso sub anything to do with zero in, do we? Does this just come from the way we initially write the Frobenius series? I was looking at the past papers and they seemed to take it this way but I just wanted to check....

Thank you!

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# A few problems with the operator method .

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