Solution
= Solution
Rearrange as $y'+(x-1)y=x-1$ and put $w=y-1$. The resulting <linear differential equation> is $w'+(x-1)w=0$, so
$$
\boxed{y=1+C\exp\left[-\frac12(x-1)^2\right].}
$$
The initial condition gives $C=1$. Its graph is a <Gaussian function> above the horizontal asymptote $y=1$, symmetric about $x=1$, with its maximum $y=2$ there. It rises for $x<1$ and falls for $x>1$, since $y'=-(x-1)e^{-(x-1)^2/2}$.