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Exercise 107

Avg difficulty 2.5

A population xx of rabbits on an island is modeled by x′=x−(1 ⁣/ ⁣1000)x2x' = x- \bigl(\nicefrac{1}{1000} \bigr) x^2, where the independent variable tt is time in months. At time t=0t=0, there are 40 rabbits on the island.

  1. Find the solution to the equation with the initial condition.
  2. How many rabbits are on the island in 1 month, 5 months, 10 months, 15 months (round to the nearest integer)?

Lebl, Notes on Diffy Qs, §1.3 Separable equations, exercise 107

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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.