Hello,

As I am almost done with my SoC proposal, and I seem to have a couple of 
days off before my hectic academic schedule again, I was looking at adding 
basic support for partial differential equations. This is because, in my 
proposal, I would have to solve PDE's at some point and it would be really 
good, if it could just add them as hints, in the PDE Module, rather than 
trying to write support then. I wouldn't want to make it solve all types of 
PDE's but just a couple of PDE's that I want it to solve. If anyone else 
wants to add support for different PDE's it can be done then, or as a 
complete SoC proposal in itself.

The corresponding PR can be seen at https://github.com/sympy/sympy/pull/1970 
.    <https://github.com/sympy/sympy/pull/1970>

It now solves first order linear homogeneous Partial Differential Equations.

The problems that I'm facing right now are:

1. Refactoring code: If you look at my commits, you could see that a vast, 
(I'd dare say all) , amount of code is copied from dsolve and the first 
part of classify_ode. However I do understand each and every line of code, 
and I haven't simply copied it blindly. I'd like suggestions to overcome 
this problem. I was thinking of something like a separate helper module, 
that contains dsolve and classify_ode , and calls hints from both the pde 
and ode module, (an argument can be passed to dsolve) in the helper module, 
that solves it as a pde or an ode.

2. Tests:  Do I need to add tests for classify_pde and pdesolve right now? 
I've added only one hint right now, and wouldn't tests for that hint be 
enough?

I would like this PR to be merged, in some form before May 27th, because it 
would be a really good help for my project if it gets selected. Even 
otherwise, it would be a valuable addition to sympy.

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