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

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

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    $\begingroup$ See the first example in tutorial Nonlinear IVP and BVPs $\endgroup$
    – kglr
    Oct 31, 2012 at 17:15
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    $\begingroup$ You might realize this already, but this isn't a standard population model like the logistic unless you take $R<0$. $\endgroup$
    – Chris K
    Feb 15, 2017 at 15:08

1 Answer 1

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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}]

manipulation ui for plot

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