  We investigate diffusion equations which have concentration dependent
diffusion coefficients with physically two relevant Ans\"atze, the self-similar
and the traveling wave Ansatz. We found that for power-law concentration
dependence some of the results can be expressed with a general analytic
implicit formulas for both trial functions.
  For the self-similar case some of the solutions can be given with a formula
containing the hypergeometric function. For the traveling wave case different
analytic formulas are given for different exponents.
  For some physically reasonable parameter sets the direct solutions are given
and analyzed in details.
