In Problems 11–14, solve the related phase plane differential equation for the given system. Then sketch by hand several representative trajectories (with their flow arrows).
The solution is .
Here the system is:
And the phase plane equation is:
Here the equation is .
Solving by variable separating. Then,
Since the solutions are centered at (1,1). And line y = x.
Therefore, the solution is .
A house, for cooling purposes, consists of two zones: the attic area zone A and the living area zone B (see Figure 5.4). The living area is cooled by a 2 – ton air conditioning unit that removes 24,000 Btu/hr. The heat capacity of zone B is per thousand Btu. The time constant for heat transfer between zone A and the outside is 2 hr, between zone B and the outside is 4 hr, and between the two zones is 4 hr. If the outside temperature stays at , how warm does it eventually get in the attic zone A? (Heating and cooling buildings was treated in Section 3.3 on page 102.)
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