# Need help separating ODE

• Feb 19th 2013, 04:14 PM
colerelm1
Need help separating ODE
How would I separate this equation? I have the solution but I don't know how they arrived there:

$\displaystyle dy/dt = ry(1-(y/K))$

separated form:

$\displaystyle dy/dt = (r/K) * y(K-y)$

Thank you
• Feb 19th 2013, 04:22 PM
HallsofIvy
Re: Need help separating ODE
Quote:

Originally Posted by colerelm1
How would I separate this equation? I have the solution but I don't know how they arrived there:

$\displaystyle dy/dt = ry(1-(y/K))$

separated form:

$\displaystyle dy/dt = (r/K) * y(K-y)$

Thank you

That's not a "separated form" at all! If you want to "separate" $\displaystyle dy/dt= ry(1- y/K)$ you can do it simply by dividing both sides by y(1- y/K).

But what they have done here is the simple algebra "get common denominators and subtract fractions":
$\displaystyle 1- \frac{y}{K}= \frac{K}{K}- \frac{y}{K}= \frac{K- y}{K}$.
• Feb 19th 2013, 04:28 PM
MathJack
Re: Need help separating ODE
multiply through ry, factor out r/K leaving, r/K(ky - y^2), which equals r/K(y(K - y))