Again consider the problem

It can be showed that the exact solution y=y(t) is

We now try to find inner and outer approximations to the problem:

*1)* If we let we get the unperturbed problem

By searching for the solution that fulfills the *outer boundary condition*

we get an outer approximation

that well agrees with the solution for “large” *t *(*t *close to* 1*)*.*

2) For “small” t (*t* close to 0, belongs to the *boundary layer*) a good inner approximation is

We will in part 12 examine how to find this.