  The general Helfrich shape equation determined by minimizing the curvature
free energy describes the equilibrium shapes of the axisymmetric lipid bilayer
vesicles in different conditions. It is a non-linear differential equation with
variable coefficients. In this letter, by analyzing the unique property of the
solution, we change this shape equation into a system of the two differential
equations. One of them is a linear differential equation. This equation system
contains all of the known rigorous solutions of the general shape equation. And
the more general constraint conditions are found for the solution of the
general shape equation.
