Solving the differential equation of bass diffusion model using Mathematica

Question

http://www.bassbasement.org/F/N/FMB/Pubs/Bass%201969%20New%20Prod%20Growth%20Model.pdf About the bass diffusion model, you can refer to the link given above. It's used to predict the adoption of new products.

Using the method below and the condition that F(0)=0, I want to get F(t), and F'(t)

  DSolve[{F′(t)=p+(q−p)∗F(t)−q∗(F[t])^2 }, F,t]

Any suggestions? Please post your answer here.

Answer 1

k = DSolve[{f'[t] == p + (q - p) f[t] - q f[t]^2,  f[0] == 0}, f, t]

Please ... try to read the manuals!

Edit

Perhaps Plotting it requires some expertise:

g[x_?NumericQ] := (f /. k[[1]] /. {p -> 1/3, q -> 2/3})[x]
Plot[{g[t], g'[t]}, {t, 0, 8}, PlotRange -> Full]