- #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-AP2
2. dP/dt=kP(M-P)
using P=Po 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-AP2 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
etk-APT=P
loge(tk-APt)=P
eP=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-AP2.
Thanks for reading this, I am not giving up and will continue to work on it now.