Following your answer I get: x^2*e^x*y=(1/2)e^2x

+ C Mr F adds the + C. The arbitrary constant of integration - so often overlooked - is essential to the solution!
This is where I solve for y right?

Mr F says: Yep, but you'll only get half the answer without the + C.
Doing this I get: y=((1/2)e^2x)/(x^2*e^x))

Which equals: y=1/(2x^2)*e^x

Where do I get the second part from? I should have:

y=1/(2x^2)*e^x[B]+(c/x^2)*e^-x

Mr F says: Hate to say I told you so . *You* only got half the answer because you forgot the arbitrary constant of integration.