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.


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Question Number 202094 by otchereabdullai@gmail.com last updated on 20/Dec/23

$A c o m p u t e r s y s t e r m h a s a m e m o r y$ $l e a k i s s u e c a u s i n g i t s u s a g e t o$ $i n c r e a s e o v e r t i m e . t h e r a t e o f$ $m e m o r y u s a g e g r o w t h i s d i r e c t l y$ $p r o p o r t i o n a l t o t h e d i f f e r e n c e$ $b e t w e e n t h e c u r r e n t m e m o r y u s a g e$ $a n d t h e s y s t e r m s m a x i m u m m e m o r y$ $c a p a c i t y . W r i t e o n e O D E a n d o n e$ $P D E t h a t m o d e l s t h e m e m o r y u s a g e$ $g r o w t h .$
Commented by mr W last updated on 20/Dec/23

$C = m a x i m u m m e m o r y c a p a c i t y$ $M = c u r r e n t m e m o r y u s a g e$ $t h e O D E i s :$ $\frac{d M}{d t} = k (C - M)$ $a P D E {d o e s n}^{'} t e x i s t, b e c a u s e M$ $o n l y d e p e n d s o n o n e v a r i a b l e, t h e$ $t i m e t .$
Commented by otchereabdullai@gmail.com last updated on 20/Dec/23

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