This note is concerned with the study of explicit solutions to stochastic differential equations. Previously, Doss and Sussman showed that the unique strong solution to the scalar Itô equationXcan be represented as a function ρ of a Brownian motion and an auxiliary stochastic processYtdetermined, for every path ofby ordinary differential equation (ODE). ρ itself is determined by a second differential equation. Now, it will be shown thatXcan be solved explicitly aswithf(.) being a continuous real valued function, providedsolves a differential equation related to the one defining ρ as well as a simple reaction-diffusion equation strongly. In particular, for a given dispersion coefficient σ(.), there will be a class drift coefficientsb(.) are provided. The corresponding explicit solutionxtfor any given dispersion σ is also supplied