Loewy Decomposition of Linear Differential Equations

As the most complete text on closed form solutions of linear partial differential equations, this book's coverage of the generalization of Loewy's decomposition includes more than fifty worked out examples and exercises in addition to their solutions.

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.