Answer
$y=Ce^{-\frac{x^2}{2}} +100$
Work Step by Step
Start by separating the y and x terms to each side
$y'= 100x -xy$
$\frac{1}{100-y} dy = xdx$, take a negative out of the y denominator
$\frac{1}{y-100} dy = -xdx$
Integrate
$ \int \frac{1}{y-100} dy= \int -xdx$
$ \ln|y-100| = -\frac{x^2}{2} +C$
Exponentiate both sides
$y-100= e^{ -\frac{x^2}{2} +C}$ , Let e^C= C.
$y=Ce^{ -\frac{x^2}{2}} +100$
