I saw this in a book:

,

can be simplified to , if one is interested only in the time scale slower than ,

I don't know how this is got, could someone help me with it? Many thanks!

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- March 7th 2010, 08:35 PMwclaymansimplification of ODE
I saw this in a book:

,

can be simplified to , if one is interested only in the time scale slower than ,

I don't know how this is got, could someone help me with it? Many thanks! - March 8th 2010, 11:06 AMCoomast
- March 9th 2010, 02:47 AMwclayman
Thanks! I get it.

- March 9th 2010, 09:23 AMchisigma
The DE can be written as...

(1)

... whose solution is...

(2)

... where...

(3)

If the exponential terms in (2) and (3) can be approximated at 1 so that is...

(4)

Kind regards

- March 12th 2010, 11:54 PMwclayman
- March 13th 2010, 12:43 AMchisigma
What is [for me] difficult to understand is why Coomast sets in His post ... the same to say that is a constant (Nerd)...

Kind regards

- March 13th 2010, 05:25 AMwclayman
I'm not sure now, ...

The author of that book is coming to visit the day after tomorrow, I'll take that chance and consult him directly. After that I will post the what he says to me.

I strongly suspect he had some typo or something! That solution is wrong.