ABSTRACT
The method of separation of variables is a well-established technique for solving ordinary differential equations. This method is easily adaptable to almost all linear homogeneous partial differential equations with constant coefficients in canonical form, and exhibits the power of the superposition principle to construct the general solution of such equations. Since linear first-order partial differential equations can always be solved by the method of characteristics, the method of separation of variables is usually applied to solve higher-order partial differential equations. The basic idea of this method is to transform a partial differential equation into as many ordinary differential equations as the number of independent variables in the partial differential equation by representing the solution as a product of functions of each independent variable. After these ordinary differential equations are solved, the method reduces to solving eigenvalue problems and constructing the general solution as an eigenfunction expansion, where the coefficients are evaluated by using the boundary conditions and the initial conditions. In most cases the solution is written in terms of a series of orthogonal functions.
