**Example:** Consider the problem

We insert y=y(t),

in the equation and get

and

We compare powers of :

Note that:

*(i)* the general solution is

*(ii)* with the boundary value

we get the solution

but then the boundary value

is not fulfilled.

*(iii)* withe the boundary value

we get the solution

but then the boundary value

is not fulfilled. We conclude that regular perturbation does not always work.