Chapter 7.9, Problem 52E

a.

To determine

To Find: The equilibrium solution for the given differential equation.

b.

To determine

To sketch: The direction field for the differential equation $y^{\prime }\left(t\right)=y\left(2-y\right)$ for $t\ge 0$ with the equilibrium solution.

c.

To determine

To sketch: The direction field for the differential equation $y^{\prime }\left(t\right)=y\left(2-y\right)$ for $t\ge 0$ with the initial condition $y\left(0\right)=1$.