The DE is...

(1)

... and we are searching for a solution of the form...

(2)

... so that is...

(3)

Now in order to proceed we suppose to know . Inserting (2) and (3) in (1) we obtain first...

(4)

... and for ...

(5)

Increasing n we obtain then...

(6)

... and for ...

(7)

All other are 0 so that is...

(8)

Kind regards