If we suppose that the general solution is analytic in , it can be written as...

(1)

With this substitution the DE becomes...

(2)

The fact that the coefficient of every power of in (2) must vanish means that...

(3)

... so that is...

(4)

The (4) is very useful because once You know and [that can be derived fron the 'initial conditions'...] with it You can derive all the . The general solution is on the form...

(5)

... where is an 'even' function the coefficients of which are derived from and is an 'odd' function the coefficients of which are derived from , in both cases using (4)...

Kind regards