Solve this second order series example:. y''-xy'+2y=0. It must be solved by power series, with a center a, finding the recurrent formula, and two linearly independent solutions.

For the problem presented, this is what it would look like if you combine the terms of the series 2 c0 x0 + 2 c2 x0 + ∑ n=1 ∞ [ a n+2 (n+1) (n+2) - an n - 2 an ] = 0

And then ...

2c0 + 2c2 = 0 and c2 = - c0

So it would go something like this.

Y = (1 - x2) c0

I am hoping that this answer has satisfied your query about this specific question.