I am working on solving a very complex differential equation. I believe I have a solution and am currently trying to check the solution I have to see if it is correct. the method I am using right now is to assign all of the derived expressions to variables and then ask Maple if my solution satisfies the differential equation. That is to say, I do something similar to the following:
x := solution :
is(left_hand_side_of_differential_equation = right_hand_side_of_differential_equation)
When I do this and ask Maple to evaluate the is() statement, my computer (which has a 64-bit processor running the 64-bit version of Maple with 8 GB of RAM and a 2.67 GHz dual core processor) cranks on it for a very long time (~15 hrs) without getting a solution.
My question is how do I determine what is taking so long or is there some way to get an estimate of how long the calculation will take? I have tried breaking down the is() statement into several steps and have determined that the hold up is in simplifying the left hand side of the differential equation, but other than that, I have no idea. Ultimately, I would like to know if Maple is caught in some sort of infinite loop or something where it will never produce an answer or if given enough time, it will find a solution. If it's just a matter of having enough time, I have the option of using the supercomputer available to me as a student; however, I would kind of like to know if this will even help me since there is some things I would have to learn in order to do that.