Graphical solution of special kinetic differential equations

A system of homogeneous linear differential equations describes the time evolution of many dynamic systems in physics. chemistry, and biology (e.g. radioactive decay, chemical kinetics of monomolecular reactions, etc.). A graph-theory approach for the direct solution of this system represented by an acyclic reaction graph is elaborated. Applying this simple method one can construct the time-dependent solution immediately from the corresponding reaction graph.I would like to express my thanks to Drs. Z. Slanina and P. Hadrava for many helpful discussions and critical comments concerning the subject of this communication. I am greatly indebted to Prof. V. Kvasnika for all the support and understanding he has given to my work in this field.