Question: 1. Consider dp/dt =0.001P(800-P) A. Find the general solution B. Solve the initial value problem when P(0)=400 C. Solve the initial value problem when P(4)=0

1. Consider dp/dt =0.001P(800-P)

A. Find the general solution

B. Solve the initial value problem when P(0)=400

C. Solve the initial value problem when P(4)=0


2. Consider dp/dt= 0.001P(800-P)-k, P(0)=750. What value of k keeps P(t) constant?


3. Consider dx/dt= (x-1)(x-2)^2(x-3)^3

A. Find all the equilibrium solutions.

B. For each equilibrium solution, determine if it is stable, unstable, or semi-stable.

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