Carrying capacity for a population (logistic deq)

[Jsorenson317]

I'm trying to find carrying capacity of a population and not having any luck.
Initial population is 400, initial death rate is 8, and initial birth rate is 10.
D=bP^2 is the death rate, B=aP is the birth rate.
This satisfies the equation
dP/dt=kP(M-P)
(aka logistic differential equation)
Help would be much appreciated, thank you and have a nice day

 

[Ishuda]

I'm trying to find carrying capacity of a population and not having any luck.
Initial population is 400, initial death rate is 8, and initial birth rate is 10.
D=bP^2 is the death rate, B=aP is the birth rate.
This satisfies the equation
dP/dt=kP(M-P)
(aka logistic differential equation)
Help would be much appreciated, thank you and have a nice day

Find P
\(\displaystyle \int_{P_o}^{P(t)}\,\, \dfrac{dP}{P\, (M-P)}\, =\, \int_{t_o}^t\, \,k\, dt\)

EDIT: And don't forget you can consolidate constants if necessary, i.e.
f(x) + a = x + b
can be converted to
f(x) = x + c
where
c = b-a