1. ## autonomous equation

I have the following equation:

$\displaystyle dN/dt = 6- {1/3}N(t), N(0) = 2$

My question is how I should treat N(t). The question is also looking for the equilibrium points. Here's what I did when I treated N(t) as a variable:

$\displaystyle 6-1/3N(t)=0$
$\displaystyle 6= 1/3N(t)$
$\displaystyle N(t)= 18$

Am I on the right track?

2. Hi
Yes it's the rigth track !

PS : sorry for my english I'm french ^^

Solution : N(t)=18+Cexp{-t/3} where C lives in R

Or N(0)=2 so 2=18+Cexp(-t/3) and you find C

3. The question also asks to solve the equation. How do I go about doing that?

4. Originally Posted by jschlarb
The question also asks to solve the equation. How do I go about doing that?
It's a linear first order equation. You can always solve these by using an integrating factor.

-Dan