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.
Loewy's results for ordinary differential equations.- Rings of partial differential operators.- Equations with finite-dimensional solution space.- Decomposition of second-order operators.- Solving second-order equations.- Decomposition of third-order operators.- Solving third-order equations.- Summary and conclusions.- Solutions to the exercises.- Solving Riccati equations.- The method of Laplace.- Equations with Lie symmetries.