Exact closed solutions of the following equation of diffusionym (∂c/∂x) = D ∂ (yn ∂ c/∂y)/∂y where m and n are considered to be independent, are obtained for the following cases: (1) diffusion from a line-source embedded in a smooth surface; (2) diffusion from a smooth surface; (3) vapor concentration in the wake of an evaporating surface. The solutions for Cases (1) and (2) belong to the similarity-solution category. Dimensional analysis has been used in the systematic search for such solutions in as concise a manner as possible. The solution for Case (3) can be obtained from those for Cases (1) and (2). Diffusion in Couette flow is given as an example.