= Solution
In <delayed carbon-dioxide ventilation feedback>, $P$ is the effective <carbon dioxide>[carbon-dioxide] <partial pressure>[partial pressure] of the lumped body compartment. Its stored <carbon dioxide>[carbon-dioxide] amount is proportional to $P$, with effective capacitance $K$, so $K\,dP/dT$ is its accumulation rate. Metabolism produces <carbon dioxide> at rate $M$. <pulmonary ventilation>[Ventilation] removes it at a rate proportional to <partial pressure>[partial pressure] <times> <pulmonary ventilation>[ventilation], $P\dot V$, with gas-conversion constants absorbed into the model coefficients. The <equation> is therefore a one-compartment <carbon dioxide>[carbon-dioxide] balance: \b[production minus respiratory removal equals accumulation]. It idealizes mixing and treats metabolic production as constant over the <time> scale of interest.
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