Partial Differential Equations: Exact Solutions Subject to Boundary Conditions This document gives examples of Fourier series and integral transform (Laplace and Fourier) solutions to problems involving a PDE and boundary and/or initial conditions. It also describes how, for certain problems, pdsolve can automatically adjust the arbitrary functions and constants entering the solution of the partial differential equations (PDEs) such that the boundary conditions (BCs) are satisfied. - Maple Programming Help

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Partial Differential Equations: Exact Solutions Subject to Boundary Conditions
This document gives examples of Fourier series and integral transform (Laplace and Fourier) solutions to problems involving a PDE and boundary and/or initial conditions. It also describes how, for certain problems, pdsolve can automatically adjust the arbitrary functions and constants entering the solution of the partial differential equations (PDEs) such that the boundary conditions (BCs) are satisfied. 

Notes on this PDE and Initial Values / Boundary Conditions Problem

Given a problem with PDEs and some BCs, note the following:

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Depending on how you write a general PDE solution, it becomes possible or nearly impossible to adjust it to match the BCs.

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Certain particular PDE solutions are frequently easier to adjust than general solutions.

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Some combinations, classified in the literature, of "certain types of PDEs" with "certain type of BCs" can be solved systematically by writing the PDE solution in a special form.

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By passing PDEs alone to pdsolve, it is not possible to predict the form of the PDE solution. On the other hand, pdsolve accepts a HINT argument so that solutions of a "certain type" can be requested.