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Unformatted text preview: we use the velocity v = x (t), we ﬁnd the diﬀerential equation
dv
mg + γ v + m
= 0.
dt
This is an ordinary diﬀerential equation of ﬁrst order because it involves just the ﬁrst derivative of the
velocity v = v (t).
Let P = P (t) denote the size of a population at time t. If we assume that the rate of change of the size
if proportional both to the size of the population as well as the diﬀerence from the maximal sustainable size
K of the population, then we ﬁnd the diﬀerential equation
P
dP
−r P 1 −
+
= 0.
K
dt
This is an ordinary diﬀerential equaiton of ﬁrst order because it involves just the ﬁrst derivative of the
population size P = P (t).
mg + γ...
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 Spring '09
 EdrayGoins

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