# logistic growth equation

• May 16th 2011, 07:25 AM
Val92
logistic growth equation
Hi, I came across the following differential equation:

dx(t)/dt=rx(t)*(1-(x(t)/K))

I am not to sure how to solve it. If i separate the variables i get:

dx(t)/[rx(t)*(1-(x(t)/K))]=dt

I dont know how to integrate this

THanks for you help
• May 16th 2011, 07:44 AM
Prove It
Use partial fractions.
• May 16th 2011, 07:44 AM
HallsofIvy
Use "partial fractions".
$\frac{1}{x(1- x)}= \frac{A}{x}+ \frac{B}{1- x}$
for some constants A and B.

I suggest you leave r on the right side of the equation with dt.