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Please solve these 2 questions step by step trying to learn for an exam. 1.Find an...

Please solve these 2 questions step by step trying to learn for an exam.

1.Find an explicit solution of the following differential equation. y' =xy-xy^2, y(0) =3

2. Suppose a population satisfies, dP/dt = 0.02P-0.00005P^2; P(0) =40 =P0, Where t is measured in Years.

a) what is the carrying capacity M?

b)for what values of P is the population increasing the fastest?

c)Given the solution of the differential equation. P(t) =M/1+Ae^-0.02t, where M is the carrying capacity and A = M-P0/P0. When will the population reach 50% of the carrying capacity?

Math   Calculus   
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