# Continuous Model

• April 1st 2010, 11:25 AM
heebee
Continuous Model
This is actually a problem for my calculus class but it's mostly diff. eq.

Given I'(t)=aI(N-I) with the initial condition I(0)=1

solve this equation and show that the solution can be written as:

I(t)=N/(1+Be^(-aNt))

any help would be greatly appreciated.
• April 1st 2010, 04:44 PM
zzzoak
$\frac{dI}{dt}$ = $aI(N-I)$
$\frac{dI}{aI(N-I)}$ = $dt$
Try to find
$\frac{1}{aI(N-I)}$ = $\frac{z1}{aI}$ + $\frac{z2}{N-I}$.
Find z1 and z2.
Integration give left side will be two functions ln, right t+C.
• April 1st 2010, 06:39 PM
heebee
so it looks like I'm to use fractional decomposition. Which Still has me stumped.