2nd Order, Homog., Reduction of Order

Hey guys! I was assigned some work this weekend in my Applied Math I class where we are doing DEs.

This question is a two part problem. I understand how to do the second part, but I'm getting stuck on the first part.

The question is...

(x^2)(y'') + (x)(y') - (y) = 0

Here is an image of my work.... I was wondering if I can get some guidance, see where/if I'm going wrong. Under the dotted line is to check my work, but I can't get it to equal zero...

http://i.imgur.com/5qiDg.jpg

Re: Looking for help (2nd Order, Homog., Reduction of Order)

I believe that the derivative of $\displaystyle \frac{d}{dx} \left(\frac{1}{x}\right)$ is $\displaystyle - \frac{1}{x^2}$ and of $\displaystyle \frac{d}{dx} \left(\frac{1}{x^2}\right) = -\frac{2}{x^3}$.