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# pertubation method - first order ODE watch

1. Let where .

So then

We expand in a pertubation series

Inserting this into (1)

Inserting into initial condition

Now let

Then

That is

Subtracting 1 from both sides and diving the rest with we get

One more time let

Then

if we repeat the procedure we realise that also

We now determine ...

subsequently by solving the equations that we get by comparing terms containing the same power of .

I'm unsure what to do now, as for I need to integrate

however my equation for is:

i.e. really complicated, and coupled with other functions.

Does anybody have any idea what I can do from here?

2. (Original post by sexyzebra)

Inserting this into (1)

I may be being thick here but at leading order doesn't

?
I may be being thick here but at leading order doesn't

?

Your not being thick at all, I'm the thick one Thank you for pointing that out. I have edited that above to avoid confusion, however I now seem to have the same situation for

since my equation for is:

and I'm not sure how to integrate this...
4. (Original post by sexyzebra)

I'm unsure what to do now, as for

These are also wrong. Your are missing .
You also can now workout term.

In terms of actually doing the intergartion I have no idea. You could try subbing the other two equations in and look for cancelling. They are hideous equations. If they gave you those equations then thats either evil or there is some other infomation or you have worked them out yourself check them (based on your ability to equate coefficeints of ).

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