Homogeneous nucleation under isothermal conditions is modeled at the kinetic level. A Fokker-Planck-like equation with nonlinear coefficients that describes this process is solved analytically by a method based on boundary-layer theory combined with the Green's-function technique. Computing the fundamental solution (propagator) of the suitably transformed governing equation, the distribution function of newly forming clusters is obtained in approximate form. Via this quantity, other important characteristics--such as nucleation rate, integrated flux, or time lag--of the nucleation are determined. It is shown that our results are in much better agreement with purely numerical simulations and experimental data than other previous analytical approaches.