Solving linear two variable functional equations with computer (Q1888651)

\textit{Zs. Páles} [Aequationes Math. 43, 236--247 (1992; Zbl 0755.39005)] presented a method for reducing linear functional equations \(\sum^n_{j=0}h_j(x,y)f_j[g_j(x,y)]=F(x,y)\) on a nonempty open set \(\Omega\) (the \(f_j\) are real valued unknown functions, sufficiently often differentiable on \(g_j(\Omega)\; (j=1,\dots,n)\)) to linear differential-functional equations. The author continues by offering a method to reduce the latter to infinitely many ordinary linear differential equations (by keeping \(y\) constant) whose order is in many cases smaller than that of the differential functional equations and easier to solve. Examples are given, including an equation solved by a MAPLE computer program (``feqsolve'', its source code is downloadable from www.uni-miskolc.hu/matha).