I was trying to solve a system of eight cubic equations, with eight variables. Note that the particular solutions should exist and my goal is to find all  possible solutions using solve. However, when executing, the solve keeps running for a whole day and did not throw any results. I also set the parameter infolevel[solve] to be 3 and find out that it is stuck in the step "GroebnerBasis: computing a factored plex basis using Groebner[Solve]". Can anyone tell me how to deal with that? Here's the Maple file.

solve_test.mw

I was trying to solve a system of polynomial equations, which contains three equations and six variables $a_0,a_1,a_2,b_0,b_1,b_2$. However, as I swap the variable name, Maple solve function gives me a totally different solutions. Only the solutions before swapping the variables are useful for the problem I study. I have already attached the file. Could anyone tell me if the choice of variable name really matters, or if i just misuse this function?

Choice_of_name_infolevel.mw

polysols(diff(u(x), x) = u(x)^2 - 1) produces no results, while it can be verified by direct observation that u(x) = 1 is a polynomial solution.