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
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.