How to plot population growth model?

Question

How would I draw the graph of a function dy/dt=((Ry^2)/T)-Ry in Mathematica?

I have tried a few times but the constants are confusing me.

Answer 1

You can get rid of the arbitrary constant of integration by imposing an initial condition.

dfeq = {y'[t] == R (y[t]^2/T - y[t]), y[0] == 1};
First@DSolve[dfeq, y[t], t]

{y[t] -> T/(1 - E^(R t) + E^(R t) T)}

Manipulate[
   Plot[T/(1 - E^(R t) + E^(R t) T), {t, -1., 1.}, 
        Exclusions -> (-E^(R t) + E^(R t) T == -1)],
   {{R, -1.2}, -2, 2}, 
   {{T, 0.3}, -1, 1}]