Hello, first time poster!
I need help to solve a linear differential equation explicitly.
Apparently this is a classic population-equation xn+1-xn=r(K-xn) where n is the generation, K is the supporting capacity (the maximum number of animals in a given enviroment).
Given: K=240, x0=130, r=0,25
I did solve this as recursion(?) in excel and I got some values which seemed okey.
When I tried to solve this my general solution was Ce2x and my particular solution was 130e2x ,however, the values are not the same when I'm testing it to my recursive values. I tried to transform it to the form y'+ay=0. Does anyone have an idea what to do here?
thanks in advance!