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The evolution of a population with constant migration rate M is described by the initial value problem dP = kP + M. P(0) = Po- (a) Solve this initial value problem; assume k is constant. (b) _Examine the solution P(t) and determine the relation between the constants k and M that will result in P(1) remaining constant in time and equal to Pg- Explain, on physical grounds, why the two constants k and M must have opposite signs to achieve this constant equilibrium solution for P(t).

The evolution of a population with constant migration rate M is described by the initial value problem dP = kP + M. P(0) = Po- (a) Solve this initial value problem; assume k is constant. (b) _Examine the solution P(t) and determine the relation between the constants k and M that will result in P(1) remaining constant in time and equal to Pg- Explain, on physical grounds, why the two constants k and M must have opposite signs to achieve this constant equilibrium solution for P(t).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The evolution of a population with constant migration rate M is described by the initial value problem dP = kP + M. dt P(0) = Po. (a) Solve this initial value problem; assume k is constant. (b) Examine the solution P(t) and determine the relation between the constants k and M that will result in P() remaining constant in time and equal to Po- Explain, on physical grounds, why the two constants k and M must have opposite signs to achieve this constant equilibrium solution for P(t).
Transcribed Image Text:The evolution of a population with constant migration rate M is described by the initial value problem dP = kP + M. dt P(0) = Po. (a) Solve this initial value problem; assume k is constant. (b) Examine the solution P(t) and determine the relation between the constants k and M that will result in P() remaining constant in time and equal to Po- Explain, on physical grounds, why the two constants k and M must have opposite signs to achieve this constant equilibrium solution for P(t).
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