why i need to solve INitial value ordinary differential equation involvin small parametre?

Question

my question releated with higher mathematics.

Answer 1

Could you tell us a little more about the equation, give us some more background? It's not clear what you want to know.

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If I understand your email properly, you're essentially asking for an application of peturbation theory (I'm assuming e is your small parameter here). In general, one seeks to solve a problem which is of the form

y^(n)(x) = f(x, e)

by looking at the solution to

y^(n)(x) = f(x, 0)

and using it to approximate the first problem (it is assumed the solution for e = 0 is easy to find).

Peturbation theory methods are used in areas such as quantum mechanics, fluid mechanics and chemistry, but these are not trivial problems to explain (they're outside my direct training and really need an expert).

You could always try the entry at Wikipedia and start from there.