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.