2nd Order DE - Power series

[bhajee]

After setting out in the sums and collecting the terms in x^j I'm left with a series of expressions in
a_2, a_3 etc as I believe i'm supposed to. However my first expression reads
2a_{2}+2a_{1}+a_-_{1}=0

Now i'm told that
y(o) = 1 and
y'(o) = 0
I think this means that
a_0 = 1
and
a_1 = 0

does this mean that
a_-_1 = x?

(My other expressions are
6a_3+6a_2+a_0=0
and
24a_4+12a_3+a_1=0)

i'm always left with an
a_-_1
when finding the other
a_{j}'s

[Dr Transport]

usually, negative subscript coefficients are set equal to zero initially in series solutions for differential equations.