- #1
member 428835
Homework Statement
Solve to order ##\epsilon## $$\epsilon d_x(xd_xf)-xf=0$$ subject to ##|f(0)|<\infty## and ##f(1)=1## via matched asymptotic expansions.
Homework Equations
Nothing comes to mind.
The Attempt at a Solution
Perform a matched asymptotic analysis. In this case when I take a series expansion $$f = \sum \epsilon^nf_n$$ the governing ODE yields the following two weighted equations $$xf_0=0\\
d_xf_0 - xf_1 + xd^2_x f_0=0.
$$
Notice the first equation implies ##f_0=0##. This is where I am stuck. Any help?
For the inner part I believe an appropriate substitution is ##x=(1-y)/g(\epsilon)##, but I thought this change of coordinates was typically introduced after first making an expansion and solving for the outer part.
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