- #1

defaultusername

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## Homework Statement

I feel so stuck.

Given the Logistic Equation:

$$\frac{dP}{dt}=kP(1-\frac{P}{A})$$

a.). Find the equilibrium solutions by setting $$\frac{dP}{dt}=0$$ and solving for P.

b.). The equation is separable. Separate it and write the separated form of the equation.

c.). Use partial fraction decomposition and then integrate both sides of the equation to solve for P.

## Homework Equations

$$\frac{dP}{dt}=kP(1-\frac{P}{A})$$

## The Attempt at a Solution

a.) $$\frac{dP}{dt}=0$$

$$⇒P=0, A$$

b.) $$⇒\frac{1}{P}+(\frac{\frac{1}{A}}{1-\frac{P}{A}})dP=k dt$$

$$⇒(\frac{dP}{1-\frac{P}{A}})=k dt$$

c.) $$⇒(\frac{dP}{1-\frac{P}{A}})=k dt$$

$$⇒P=\frac{B}{P}+\frac{C}{1-\frac{P}{A}}$$

I am not even sure if I am doing everything correctly or not. I need to find a common denominator to solve for B and C but my attempts always end up as a huge mess.