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A-computer-systerm-has-a-memory-leak-issue-causing-its-usage-to-increase-over-time-the-rate-of-memory-usage-growth-is-directly-proportional-to-the-difference-between-the-current-memory




Question Number 202094 by otchereabdullai@gmail.com last updated on 20/Dec/23
 A computer systerm has a memory     leak issue causing its usage to    increase over time. the rate of     memory usage growth is directly     proportional to the difference     between the current memory usage    and the systerms maximum memory    capacity. Write one ODE and one     PDE that models the memory usage    growth.
$$\:{A}\:{computer}\:{systerm}\:{has}\:{a}\:{memory}\: \\ $$$$\:\:{leak}\:{issue}\:{causing}\:{its}\:{usage}\:{to} \\ $$$$\:\:{increase}\:{over}\:{time}.\:{the}\:{rate}\:{of}\: \\ $$$$\:\:{memory}\:{usage}\:{growth}\:{is}\:{directly}\: \\ $$$$\:\:{proportional}\:{to}\:{the}\:{difference}\: \\ $$$$\:\:{between}\:{the}\:{current}\:{memory}\:{usage}\: \\ $$$$\:{and}\:{the}\:{systerms}\:{maximum}\:{memory} \\ $$$$\:\:{capacity}.\:{Write}\:{one}\:{ODE}\:{and}\:{one}\: \\ $$$$\:\:{PDE}\:{that}\:{models}\:{the}\:{memory}\:{usage} \\ $$$$\:\:{growth}. \\ $$
Commented by mr W last updated on 20/Dec/23
C=maximum memory capacity  M=current memory usage  the ODE is:  (dM/dt)=k(C−M)  a PDE doesn′t exist, because M   only depends on one variable, the  time t.
$${C}={maximum}\:{memory}\:{capacity} \\ $$$${M}={current}\:{memory}\:{usage} \\ $$$${the}\:{ODE}\:{is}: \\ $$$$\frac{{dM}}{{dt}}={k}\left({C}−{M}\right) \\ $$$${a}\:{PDE}\:{doesn}'{t}\:{exist},\:{because}\:{M}\: \\ $$$${only}\:{depends}\:{on}\:{one}\:{variable},\:{the} \\ $$$${time}\:{t}. \\ $$
Commented by otchereabdullai@gmail.com last updated on 20/Dec/23
Thank you prof W
$${Thank}\:{you}\:{prof}\:{W} \\ $$

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