Advanced Engineering Mathematics, 7th Edition

13.1 Separable Partial Differential Equations

INTRODUCTION

Partial differential equations (PDEs), like ordinary differential equations (ODEs), are classified as linear or nonlinear. Analogous to a linear ODE (see (6) of Section 1.1), the dependent variable and its partial derivatives appear only to the first power in a linear PDE. In this and the chapters that follow, we are concerned only with linear partial differential equations.

Linear Partial Differential Equation

If we let u denote the dependent variable and x and y the independent variables, then the general form of a linear second-order partial differential equation is given by