I use PDsolve to solve sets of PDEs analytically.

I have had tremendous success with this but recently realized that for PDEs if you manually factor out common expressions , it makes it much easier for maple to solve it.

I was wondering if there were other "tricks" like these that I might be unaware of.

Also I found this link comparing how maple compares to mathematica in solving known PDES just in case the maple developers are interested.
Results (12000.org)

I dont know if this is a well formulated question but if I had a set of PDES that have a constant appearing in them (say alpha), would there be a way to solve for the PDE such that the right had side is not zero but just has higher order order terms (say alpha^3 and higher).

For example consider (the random set of equations)
 

eq1 := alpha*diff(f(t, r), r,r) + diff(g(t, r), t) + alpha*g(t, r) = 0;
           

eq2 := alpha*diff(g(t, r), r) + diff(f(t, r), t,t) + f(t, r) = 0;

Is there a way to solve for the system of pde such that the right hand side is only terms of order alpha^3 and higher?
 

I have been using the RaiseLowerIndices to go from covectors to contravariant vectors.

RaiseLowerIndices(Contravariant_form_of _metric, One_Form, [1])

The above gives me the right answer.
But the following also gives me an answer which is different. I just dont know what it is calculating.

RaiseLowerIndices(Contravariant_form_of _metric, One_Form, [1,1]).

Could someone tell me what it is calculating?

I am trying to see if there is a way to submit maple code as a worksheet and get results back as worksheets in a cluster. 

If I have a pde with multiple constants (for example a and b) in them such that some are fixed constants (say k) and some terms are undetermined constants , how do I put that in a PDE such that Maple knows to solve the equation not for arbritary k (in case no solution exists), but any k such that k is not a function of the differentiating variable.