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
