You're looking for a solution in the form
Differentiating, we get
Substitute these for y' and y'' in the differential equation:
Then the coefficients of y are given by the recurrence
or
But we cannot assume that
and
depend on each other; we can only guarantee that the recurrence holds for n ≥ 1, so that
So in the power series solution, we split off the constant term and we're left with
so that the fundamental solutions are
and