Chapter D1.2, Problem 21E

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.

21.     $\begin{array}{c}{P}^{\prime }\left(t\right)=0.05P\left(1-\frac{P}{500}\right);P\left(0\right)=100,P\left(0\right)=400,\\ P\left(0\right)=700\end{array}$