When Will the Rabbit Population Recover After a Myxomatosis Outbreak?

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The rabbit population is modeled by the logistic equation dy/dt=2*10^-7y(10^6-y), indicating growth dynamics. After a myxomatosis outbreak, the population drops to 40% of its steady state, which is 400,000 rabbits. Eight months later, without further effects from the disease, the population is projected to recover significantly. To determine how long it will take to reach 90% of the steady state size, the differential equation must be solved. This analysis is crucial for understanding population recovery post-outbreak.
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A rabbit population satisfies the logistic equation dy/dt=2*10^-7y(10^6-y) where t is the time measured in months. The population is suddenly reduced to 40%of its steady state size by myxomatosis.
a) If the myxo' then has no effect how large is the population 8 months later?
b)How long will it take for the population to build up again to 90% of its steady state size?
 
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What have you tried so far? The first step will be to solve the differential equation to find the function y(t)
 
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