Advanced Engineering Mathematics, 7th Edition

13.6 Nonhomogeneous Boundary-Value Problems

INTRODUCTION

A boundary-value problem is said to be nonhomogeneous if either the partial differential equation or the boundary conditions are nonhomogeneous. The method of separation of variables employed in the preceding three sections may not be applicable to a nonhomogeneous boundary-value problem directly. In the first of the two techniques examined in this section we employ a change of dependent variable u = v + ψ that transforms a nonhomogeneous boundary-value problem into two BVPs: one involving an ODE and the other involving a PDE. The latter problem is homogeneous and solvable by separation of variables. The second technique may also start with a change of a dependent variable, but is basically ...