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Exercise 103

Avg difficulty 2.5

Assume that a population of fish in a lake satisfies dxdt=kx(M−x)\frac{dx}{dt} = kx(M-x). Now suppose that fish are continually added at AA fish per unit of time.

  1. Find the differential equation for xx.
  2. What is the new limiting population?

Lebl, Notes on Diffy Qs, §1.6 Autonomous equations, exercise 103

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.