A disease is spreading through the country. Let x be the number of people infected. Let the constant S be the number of people susceptible to infection. The infection rate dx is dt proportional to the product of already infected people, x, and the number of susceptible but uninfected people, S − x. a) Write down the differential equation. b) Supposing x(0) > 0, that is, some people are infected at time t ? 0, what is lim x(t). t→∞ c) Does the solution to part b) agree with your intuition? Why or why not?

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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.