Non-Homogenous second order DE Problem

My work see:
http://i.imgur.com/xgRGPfP.png

my general solution differs from that of what I get on wolframalpha by the term -x^2
see:
http://www.wolframalpha.com/input/?i=x^2y%27%27+-+2xy%27+%2B+2y+%3D+x^2

Any idea why this may be? I used Variation of parameters method to solve as it seemed like undetermined parameters was not applicable.

Question

Non-Homogenous second order DE Problem

My work see: 
http://i.imgur.com/xgRGPfP.png

my general solution differs from that of what I get on wolframalpha by the term -x^2
see:
http://www.wolframalpha.com/input/?i=x^2y%27%27+-+2xy%27+%2B+2y+%3D+x^2

Any idea why this may be? I used Variation of parameters method to solve as it seemed like undetermined parameters was not applicable.

phi · Answer

your solution includes the terms
$$ c_2 x^2 - x^2 $$
which can be written as
$$ ( c_2 -1) x^2 $$
because c2 is arbitrary, you can just write this as 
$$ c_2 ~x^2 $$

australopithecus · Answer

oh yeah blah my brain is not working atm thanks

irishboy123 · Answer

i don't see how your solution is different.   change (c2-1) to c3 and surely it is the same as the computer, absent IVP arithmetic errors?

australopithecus · Answer

yeah it isn't