This paper shows that the general homogeneous solution to equations of evolution for some infinite systems of particles subject to mutual binary collisions does not depend on a single arbitrary constant but on a potentially infinite number of such constants. This is because, as I demonstrate, a single self-excitation of a system of particles can depend on a potentially infinite number of parameters. The recent homogeneous solution obtained by Atkinson and Johnson, which depends on a single arbitrary constant, is only (...) a particular case. (shrink)