Maple 9 Learning Guide - Maplesoft

270 • Chapter 7: Solving Calculus ProblemsIf odesys is not given in the call to dsolve[interactive], thenodesys can be entered by using the interface; otherwise, the input equationsare examined and used as a starting point for the application (theseequations can be changed from within the graphical user interface).For details about the command and interface, see ?dsolve,interactiveand ?worksheet,interactive,dsolveinterface.7.3 Partial Differential EquationsPartial differential equations (PDEs) are in general very difficult to solve.Maple provides a number of commands for solving, manipulating, andplotting PDEs. Some of these commands are in the standard library, butmost of them reside in the PDEtools package.The pdsolve CommandThe pdsolve command can solve many partial differential equations. Thisis the basic syntax of the pdsolve command.pdsolve( pde, var )• pde is the partial differential equation• var is the variable with respect to which pdsolve solvesThe following is the one-dimensional wave equation.> wave := diff(u(x,t), t,t) - c^2 * diff(u(x,t), x,x);wave := ( ∂2∂t 2 u(x, t)) − c2 ( ∂2u(x, t))∂x2 To solve for u(x,t), first load the PDEtools package.> with(PDEtools):> sol := pdsolve( wave, u(x,t) );sol := u(x, t) = _F1(c t + x) + _F2(c t − x)Note the solution is in terms of two arbitrary functions, _F1 and _F2.To plot the solution you need a particular set of functions.