[tex]\epsilon[/tex]y'' - y' = 0
y(0)=0, y(1)= 1
The Attempt at a Solution
this s a perturbation problem, but i'm not sure how to go about doing it
if we let epsilon = 0 we'll go from 2nd order to first order so it's a boundary layer problem... i think
so if thats the case then i have to find the outer and inner layer
to find the outer layer i let epslon =0 and i get y' = 0
then to find the inner layer i let x=[tex]\epsilon[/tex]nX
then after a few steps i got to this:
1/[tex]\epsilon[/tex] d2y/dX2 - 1/[tex]\epsilon[/tex]dy/dX
and then solve it normally then find the general solution etc.
and also i'm letting y = y0+ epsilony1 + epsilony2...
and y' = ...
and y''= ....
and subbing them in and solving it too... i can do that, even though theres and epsilon?
and then i'm supposed to compare these together?