  We analytically solve for the time dependent solutions of various density
evolution models. With specific forms of the diffusion, drift and sink
coefficients, the eigenfunctions can be expressed in terms of hypergeometric
functions. We obtain the relevant discrete and continuous spectra for the
eigenfunctions. With non-zero sink terms the discrete spectra eigenfunctions
are generalisations of well known orthogonal polynomials: the so-called
associated-Laguerre, Bessel, Fisher-Snedecor and Romanovski functions. We use a
MacRobert's proof to obtain closed form expressions for the continuous
normalisation of the Romanovski density function. Finally, we apply our results
to obtain the analytical solutions associated with the Bertalanffy-Richards
Langevin equation.
