Consider the autonomous differential equation

$y^{\text{'}}=y(y-2)=y^2-2y$

$($a$)$ Determine all equilibrium solutions.

$($b$)$ Find all values of $y$ at which the solution curves have inflection points and determine the intervals of concavity for solution curves.

$($c$)$ Sketch the slope field corresponding to the given differential equation AND sketch a solution curve in each region determined by the equilibrium solutions.