Consider the equation form the last part
We expand y(x) in a perturbation series
Insertion in the equation yields
Insertion in the inital condition yields
Now let
Then
that is
If we subtract 1 on both sides and divide the rest with 
we get
On more time, we let
Then
and if we repeat the procedure we realize that also
We determine y0, y1, y2,…. subsequently by solving the equations that we get by comparing terms containing the same power of :
 |
 |
 |
 |
 |
 |
An approximate solution is thus
