# non linear 1st order

• May 3rd 2011, 01:12 AM
tedchou12
non linear 1st order
Hi, can anyone show me how this is done:
x' = rx - rx^2
Thanks,
Ted C.
• May 3rd 2011, 02:07 AM
CaptainBlack
Quote:

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
• May 3rd 2011, 02:14 AM
tedchou12
yes, r is a constant, separable variable? intergrate both sides?
• May 3rd 2011, 02:15 AM
Ackbeet
Quote:

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.
• May 3rd 2011, 08:55 AM
HallsofIvy
Quote:

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.