Given a pde (or a set of pdes) of multiple funcitons, is there a way to look for solutions when one of the functions is kept arbritary.

For example if I have a set of pdes with f1,f2,f3. Is there a way to see if there is a functional form for f2 and f3 such that the equation is satisfied for any f1?

Is there a way in the physics package to get my index to run from 0 to 3 instead of 1 to 4/0?

When I am setting up the coordinates in the physics package, I use the following command. And it sets it to (r,theta,phi,t).

Setup(dimension = 4, mathematicalnotation = true, coordinates = spherical)

Is there a way to change it to (t,r,theta,phi)?

It gets a bit more confusing when we are looking at rank 2 objects.

I have this tedious looking function that I want to write in terms of the other expression but the command i usually use does not work here because the expressions are not polynomials. I am wondering if there is an alternative to doing this manually.
Temp.mw

I would like to use the forget command to make maple forget all the things it remembers in each iteration of the loop.

Could someone help me with that?

More details:  I use ansatz to try to solve systems of pdes. sometimes i put the ansatzs in a list and run a loop to try to solve the set of pdes for each ansatz. Sometimes this takes up a lot of memory and maple says kernel connection is lost.