# Thread: non linear 1st order

1. ## non linear 1st order

Hi, can anyone show me how this is done:
x' = rx - rx^2
Thanks,
Ted C.

2. Originally Posted by tedchou12
Hi, can anyone show me how this is done:
x' = rx - rx^2
Thanks,
Ted C.
If "r" is a constant then this is of variables seperable type

CB

3. yes, r is a constant, separable variable? intergrate both sides?

4. Originally Posted by CaptainBlack
If "r" is a constant then this is of variables seperable type

CB
Just as an aside (since CB's method is undoubtedly the easiest): it's also a Bernoulli equation.

5. Originally Posted by tedchou12
Hi, can anyone show me how this is done:
x' = rx - rx^2
Thanks,
Ted C.
Yes,
$\frac{dx}{x- x^2}= r dt$
Integrate both sides.