How Do You Solve Complex Differential Equations in Population Growth Models?

[AngusYoung93]

Hey, everyone. I've been doing my Calculus II homework, and I've been trying these two problems for the past few hours, but I can't even seem to get started on them. A friend of mine recommended I try here because you guys are awesome.

Homework Statement

The Gompertz equation
dP/dt = P(a - b ln(P))
where a and b are positive constants, is another model of population growth.
a) Find the solution of this differential equation that satisfies the initial condition: P(0) = p(sub(0))
b) What happens to P(t) as t -> infinity?
c) Determine the concavity of the graph of P


2. The attempt at a solution

dP/dt = P(a - bQ)

where Q = ln(x)​

Homework Statement

the differential equation
dP/dt = P(10^-1 - (10^-5)P)
models the population of a certain community. Assume P(0) = 2000 and time t is measured in months.
a) Find P(t) and show that lim t -> infinity exists
b) Find the limit


2. The attempt at a solution

I do not even know where to start on this. Any help at all would be nice.

 

[Rainbow Child]

Write it as
\frac{d\,P}{P\,(a-b\,\ln P)}=d\,t
and set \ln P=u