We study the continuity and differentiability properties of the solution $\varphi $ of a linear integral equation arising in transport theory. The integral equation is described by an operator T which maps bounded functions into Holder continuous functions. T does not commute with the differential operator D. In particular, the difference $DT - TD$ introduces singularities near the boundary of the domain. We develop a method to generate a representation for any derivative $D^m \varphi $ of $\varphi $, from which we obtain a representation for $\varphi $ which explicitly demonstrates its asymptotic behavior near the boundary.