Example 1.1.1:

$D_xy=y(1-y)=y-y^2$ (the logistic model)
Solution: $D_xy=\frac{dy}{dx}=y(1-y) \Leftrightarrow \frac{dy}{y(1-y)}=dx \Leftrightarrow ... ...\vert = x+C \Leftrightarrow \ln \vert 1-\frac{1}{y}\vert = -x+C \Leftrightarrow$ Assuming $1-\frac{1}{y} \geq 0$, $1-\frac{1}{y}=e^{-x+C} \Leftrightarrow -1=e^{-x+C}y-y=y(e^{-x+C}-1) \Leftrightarrow y=\frac{-1}{e^{-x+C}-1}$