The fish population P(t) (in millions) in a large fish farm where 2 million fishes are dP - ЗР— Р2 — 2. dt harvested each year follows the differential equation %3D (a) Find all equilibrium solutions of the differential equation. For what values of P, is the population increasing with time, and for what P values is it decreasing? (b) If the initial population is P(0) = 1.5 (in millions), can we continue to harvest at the rate of 2 million fish per year indefinitely? Explain. (c) Find the solution P(t) with p(0) = 1.5.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.