Solution to differential equation

I am trying to find the analytical solution to this differential equation

dR/dt = k1*(R^k2)*(1-(R/Rmax)); R(0) = Ro

If there is an analytial solution to this differential equation then it

It is a polynomial function of R, so just develop the expression and
when you get the two terms in R (hint: one has exponent k2, the other
k2+1) you can simply apply the basic integration rule for polynomials.
It literally doesn't get easier than that.

the resulting function is:

k1/(k2+1) * R^(k2+1) - K1/[Rmax*(k2+2)] * R^(k2+2) + Ro

scion