# 2nd Order DE - Power series

1. Jul 13, 2004

### 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

2. Jul 13, 2004

### Dr Transport

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