question archive The total number y(t) of cases of AIDS (acquired immunodeficiency syndrome) diagnosed in a certain region after t years satisfies the following
The total number y(t) of cases of AIDS (acquired immunodeficiency syndrome) diagnosed in a certain region after t years satisfies the following
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The total number y(t) of cases of AIDS (acquired immunodeficiency syndrome) diagnosed in a certain region after t years satisfies the following.
y'-(3/t)y=0
(for t ≥ 1)
y(1)=125
(a) Solve this differential equation and initial condition. (Your solution will show that AIDS does not spread logistically, as do most epidemics, but like a power. This means that AIDS will spread more slowly, which seems to result from its being transmitted at different rates within different subpopulations.)
y(t)=
(b) Use your solution to predict the number of AIDS cases in the region by the year
t = 11.
_________________cases
