- #1

sara_87

- 763

- 0

## Homework Statement

[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]

^{n}X

then after a few steps i got to this:

1/[tex]\epsilon[/tex] d

^{2}y/dX

^{2}- 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?