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 *y _{0}, y_{1}, y_{2},….* subsequently by solving the equations that we get by comparing terms containing the same power of :

An approximate solution is thus