  We show that for any semilinear partial differential equation of order m, the
infinitesimals of the independent variables depend only on the independent
variables and, if m>1 and the equation is also linear in its derivatives of
order m-1 of the dependent variable, then the infinitesimal of the dependent
variable is at most linear on the dependent variable. Many examples of
important partial differential equations in Analysis, Geometry and Mathematical
- Physics are given in order to enlighten the main result.
