Suppose a student carrying a flu virus returns an isolated college campus of 1000 students. Determine a differential equation to calculate the number of students x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students who have not yet been exposed to it ?

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A: As you have asked multiple questions so that I have answered first question as per the guidelines.

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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.