A Direction Field for a Differential Equation Is Given Below $P$

question 2

Essay

A direction field for a differential equation is given below:
(a) Sketch the graphs of the solutions that have initial condition $P$ and initial condition $Q$ .
(b) Determine whether the differential equation is autonomous. Explain your answer.

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Definitions:

Alveoli

Tiny air sacs in the lungs where the exchange of oxygen and carbon dioxide takes place.

Alveolar Ducts

Tiny ducts in the lungs that connect the bronchioles and alveolar sacs, facilitating gas exchange.

Terminal Bronchioles

The smallest air passages in the lungs that lead to the alveolar ducts, playing a crucial role in the transfer of oxygen and carbon dioxide.

Respiratory Bronchioles

The smallest airways in the respiratory system, through which air passes before reaching the alveolar sacs for gas exchange.