ay'+ay=y-xy',
(a+x)y'+y(a-1)=0,
y'+[(a-1)/(a+x)]y=0
(a-1)∫dx/(a+x)=(a-1)ln|a+x|, integration factor=e(a-1)ln|a+x|=(a+x)a-1.
(a+x)a-1y'+(a-1)(a+x)a-2y=0,
(d/dx)((a+x)a-1y)=0,
(a+x)a-1y=C, where C is constant,
y=C(a+x)1-a.
PROOF
y'=C(1-a)(a+x)-a=(1-a)[C(a+x)1-a]/(a+x)=(1-a)y/(a+x),
ay'+xy'=y-ay,
ay'+ay=y-xy'.