4. Suppose that a student carrying a flu virus returns to an isolated campus of 1000 students. After this, the student body population doesn't change and students only interact with other students. In ten days there have been 5 cases of the flu on campus. Suppose y(t) is the number of people at the campus who have caught the flu after t days. Then 1000 – y represents the number of people who have not yet contracted the flu. Lets assume that the rate of spread of the flu is directly proportional to the total number of possible interactions between the these groups. In simple terms, increasing the number of interactions between the inflected and the non inflected causes the flu to spread quickly. A differential equation which represents this situation is given by: dy = ky(1000 – y) dt y(0) = 1, y(10) = 5

4. Suppose that a student carrying a flu virus returns to an isolated campus of 1000 students. After this, the student body population doesn't change and students only interact with other students. In ten days there have been 5 cases of the flu on campus. Suppose y(t) is the number of people at the campus who have caught the flu after t days. Then 1000 – y represents the number of people who have not yet contracted the flu. Lets assume that the rate of spread of the flu is directly proportional to the total number of possible interactions between the these groups. In simple terms, increasing the number of interactions between the inflected and the non inflected causes the flu to spread quickly. A differential equation which represents this situation is given by: dy = ky(1000 – y) dt y(0) = 1, y(10) = 5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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