  In the 49th International Symposium on Functional Equations, J. Acz\'el asked
for the monotonic solutions of a certain one-parameter family of functional
equations. In this short note we find that for a certain value of the parameter
the monotonic solutions are the expected ones, and that for other values this
is not so. Further, we find all continuous and continuously differentiable
solutions to the equations.

Classical Analysis and ODEs