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# Series expansion for general solution of 2nd order linear differential watch

1. I'm stuck on the following question:

I don't know how to work out the general recurrence, I've done my best attempt to get somewhat one but I know it's wrong but it's as close as I can get.

Even with my general recurrence I don't know what to do with it to get the general solution.

Here is my working (plz help):
https://imgur.com/a/FZyPw

Sry it's a mess, being at it for many hours on the same question. My general method is finding a2,a3,a4, etc in terms of a0,a1 then trying to spot a pattern from those to get a general recurrence, I don't really know what I'm meant to be doing.
2. (Original post by Sayless)
I'm stuck on the following question:

I don't know how to work out the general recurrence, I've done my best attempt to get somewhat one but I know it's wrong but it's as close as I can get.
Caveat: I have no background in this at all. That said, I think I can help.

As at A-level "write down" implies little or no working required.

To get the general recurrence relation, consider the coefficients of in the d.e.

E.g. For the y'' part it will be

Can you now complete the recurrence relation?
3. (Original post by ghostwalker)
Caveat: I have no background in this at all. That said, I think I can help.

As at A-level "write down" implies little or no working required.

To get the general recurrence relation, consider the coefficients of in the d.e.

E.g. For the y'' part it will be

Can you now complete the recurrence relation?
Thanks for the help, I managed to complete it now and yeah what you suggested is right, I had to look at the coefficients of x^n and form an equation = 0, then rearrange it for a_n+2.

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