Answer
$\frac{dy}{dt}=-3y+2$
Work Step by Step
We must write a differential equation of the form $\frac{dy}{dt}=ay+b$ such that all solutions approach $y=\frac{2}{3}$ as $t\rightarrow\infty$.
Solution:
We want to have the solution function to have slope $0$ when $y=\frac{2}{3}$. Thus,
$0=a(\frac{2}{3})+b$.
So, $\frac{b}{a}=-\frac{2}{3}$.
Hence, one such equation satisfying this criteria is
$\frac{dy}{dt}=-3y+2$.
This may be rewritten
$y'=2-3y$.
