In a seasonal growth model, a periodic function of time is introduced to account for seasonal variations in the rate of growth. Such variations could, for example, be caused by seasonal changes in the availability of food. (a) Find the solution of the seasonal-growth model dP dt = kP cos(rt − φ) P(0) = P0 where k, r, and φ are all positive constants. (b) By graphing the solution for several values of k, r, and φ, explain how the values of k, r, and φ affect the solution. What can you say about limt→∞ P(t)?

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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.