- #1

NZBRU

- 20

- 0

## Homework Statement

I need to solve two differential equations to find a population function P(t). I am able to do this with problems like Newtons law of cooling:

dT/dt=-k(T-Ta) solves to:

dT=-k(T-Ta) dt

∫1/(T-Ta)dT=∫-k dt

Ln(T-Ta)=-kt

e

^{-kt}=T-Ta

T=Ta+E

^{-kt}

However I have been presented with two hard problems which I can not do:

1. dP/dt=kP-AP

^{2}

2. dP/dt=kP(M-P)

using P=P

_{o}at t=0 find P(t) for both.

## Homework Equations

^As above, no other equations where provided, it is pretty much calculus and algebra

## The Attempt at a Solution

dP=kP-AP

^{2}dt

dP=P(k-AP) dt

1/P dP = k-AP dt

∫1/P dP = ∫k-AP dt

Ln(P)=t(k-AP)

Ln(P)=tk-APt

e

^{tk-APT}=P

log

_{e}(tk-APt)=P

e

^{P}=tk-APt

From there it just loops around. I can not think of anything else to do with it. As you can not (that I am aware of, unless you used unreals, factorise kP-AP

^{2}.

Thanks for reading this, I am not giving up and will continue to work on it now.