How to scale a logistic equation to become dimensionless?

[miclectric]

Homework Statement

I have an equation: dN/dt = N(r-a(N-b)^2) where r,a,b>0 are constants and I need to scale it to the dimensionless form dn/dtao=n(1-a(n-1)^2), however, I tried many ways and I am still unable to get it into the form. The question also suggests using n=N/c and tao=t/d as a substitution.

Homework Equations

The Attempt at a Solution

I tried to first expand out the N in the original equation and tried a separation of equation form to get the N's all on one side and dt on the other, but I can't seem to do this. I've also tried to substitute the suggested substitutions, however I can't seem to get it to the form either... :(

 

[mfb]

The Attempt at a Solution

I tried to first expand out the N in the original equation and tried a separation of equation form to get the N's all on one side and dt on the other, but I can't seem to do this. I've also tried to substitute the suggested substitutions, however I can't seem to get it to the form either... :(

Please show your work then. The given substitutions will work, you just have to find c and d (that will become clear once you simplify the equation).