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that should be
(x+1) y' - xy = x

first divide through by (x+1) right?

yes thats what i got

right so its
(1+x)e^(-x) y' - x e^(-x) y = x e^(-x)
ok?

i must admit i'm struggling a bit with these

right and integrating xe^(-x|) I got -e^(-x)(1 + x) + A

same here, so far you have.
\[\large y(x)(x+1)e^{-x}=-e^{-x}(x+1)+C \]

yea i dont know why they did that

makes no sense to me, I just asked WolframAlpha and our answer seems to be correct.

right
thanks

a typo
thanks for your help

no problem.

yes exactly, you can ignore this one during the process (-: