Thread: Urget: MacLaurin Series (i.v.) and Dawsons Equations

Hi... first, if someone would like to give me more help in the next two days, not doing my work, but at least check it, I will definitely compensate for your time.

Second, here is the problem I am struggling with...

MacLaurin for smooth solution of the I.V. problem:

Y''+ (x + (2/x)) y' + 2y = 0 , y(0) =1

and show solution is given by Dawson's integral : y(x) = (1/x) *integral(0-x)* e^((1/2)(u^2) - (x^2))

I am so lost. Should I start with Frobenius Method? How would you all do this?

I'm not sure how to proceed with this, but I've got a couple of questions/comments.

Since it's a second order ode don't we need a second initial condition for a unique solution ?
Secondly, if we are looking for a Maclaurin series, is that 2/x in the middle term going to be a problem ?