Construction Solutions of PDE in Parametric Form

A new method of construction of exact solutions for partial differential equations PDE is proposed in this article. The classical authors in mathematics used change of variables for classification of linear PDE. However, they did not notice an important property of broad class of PDE, which was discovered in Volosov’s articles 1–4 . Literature reference 3 is available for review on http://eqworld.ipmnet.ru/ This property gives the possibility of expressing PDE as AX b. This is a linear algebraic equations system with regards derivatives to old variables on new variables. This equations system has the unique solution. New identity was obtained which follows from solvability conditions of the system. The methods of the above calculations and their consequence are described in this article. Let us consider the: