Chapter D1.2, Problem 22E

Logistic equations Consider the following logistic equations, for t ≥ 0. In each case, sketch the direction field, draw the solution curve for each initial condition, and find the equilibrium solutions. A detailed direction field is not needed. Assume t ≥ 0 and P ≥ 0.

22.     $\begin{array}{c}{P}^{\prime }\left(t\right)=0.1P\left(1-\frac{P}{1200}\right);P\left(0\right)=600,P\left(0\right)=800,\\ P\left(0\right)=1600\end{array}$