Assume that in the absence of immigration and er

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0 (see Equation (1) of
Section 1.3). Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant
rate r> 0. (Use P for P(t).)
dP
kp +r
%3D
dt
What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r> 0?
dP
kp – r
%3D
dt
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Transcribed Image Text:Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0 (see Equation (1) of Section 1.3). Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r> 0. (Use P for P(t).) dP kp +r %3D dt What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r> 0? dP kp – r %3D dt Need Help? Read It
Expert Solution
Step 1

Given in the absence of immigration and emigration, the growth of a country's population P(t) satisfies 

                                                     dPdt=kP

for some constant k>0

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