No. There is (currently, but thing do change) no MATLAB utility that will alllow you to provide a fully general PDE, with your own choice of boundary conditions, on your choice of general domain, and then solve for the complete analytical solution of said PDE in closed algebraic form. This would be far too complex a problem to write a fully general code to do. In fact, you can find texts written on the subject, courses taught at various levels.
At best, there are PDE tools that will solve the problem in numerical form, using some prescibed methodology. And even there, you can find entire courses taught at the graduate level, on the various ways to solve such a problem.
Solving many ODEs becomes too difficult a problem that often no analytical closed form solution exists, and a PDE is a more complicated animal than an ODE. So unless you are willing and able to make specific assumptions about the solution (separability, for example) no closed form solution will be found for many PDE problems. And even there, you will need to do some/much of the mathematics before you throw it at some general symbolic solver.
