Diff eq, power series solns, how do i determine how many terms to pull?

[channel1]

Homework Statement

find 2 power series solutions of the given diff eq about the ordinary point x = 0
y'' - xy = 0

Homework Equations

y = (c_0)(y_1)[x] + (c_1)(y_2)[x]

The Attempt at a Solution

i can set it up to this (sorry idk out how to insert the subscripts with the summation symbols)

{sum n=2} [n (n-1) (c_n) (x ^(n-2) ) ] - {sum n=0} [(c_n) (x ^(n+1) ) ] = 0

but I am not sure how to determine how many terms i need to pull from each series

also, does it matter how many terms i pull so long as my value for k is the same for each series?

 

[vela]

You can click on the equation below to see how to write the equation:

$$\sum_{n=2}^\infty n(n-1)c_n x^{n-2} - \sum_{n=0}^\infty c_n x^{n+1} = 0$$

The first series starts with a constant term, but the second series begins with the x¹ term, so pull the constant term out of the first series and then combine the rest with the terms of the second series.