I used Maple’s odetest to check the validity of 36 exact solutions.

About half of them return zero, meaning they satisfy the ODE correctly. But the other half don’t — odetest gives nonzero expressions.

My question is:

Could there be a mistake in my assumptions, or are some of these solutions only valid under specific conditions?

I’d appreciate any clarification or suggestions.

ode-test-36.mw

Hi everyone,

I've encountered something odd while working with Maple's pdetest function. When I manually evaluate my proposed solution using eval() followed by simplify(), I get the expected identity 0 = 0, which suggests the solution satisfies the PDE. However, when I test the same solution using pdetest, it doesn't return zero. This inconsistency has left me unsure whether my solution is actually valid or if I'm missing something.

Has anyone else experienced this kind of discrepancy? Could this be due to how pdetest handles derivatives or symbolic simplification internally?

Any insights or suggestions would be greatly appreciated!

Download pde-test.mw

in some of my function i have a big problem which i can't plot thus function even i know what is the shape of plot, i have two type of ploting directly giving parameter and using explor but for this kind of plot we can't use explor so i have to give the function directly parameter but is wasting my time a lot and i can't get my plot even spending a days by changing parameter one by one, my questions is this how i can plot this kind of function without bieng a singular i need this function to be non singular is not importan about the parameter can be any number 
thanks for any help 

plots-long_term_.mw

the shape of plot must be like this but must have two of them 

I'm currently working on applying a specific method to solve a nonlinear equation. However, I've encountered a recurring issue: during the process, I often cannot determine certain parameters, which forces me to abandon the solution or switch to a different method. This has happened multiple times and is disrupting my goal of applying all intended methods consistently to a single equation.

In particular, I’m struggling to identify the correct parameters for U(ξ), which are essential for the solution. This challenge is not limited to one method I’ve faced similar problems in previous attempts, and I’m unsure why these parameters cannot be derived in some cases.

My question is: How can I manage this issue effectively? Is there a reliable way to predict or determine whether the necessary parameters will emerge correctly before fully applying a method?

I would greatly appreciate any insights or strategies you could share to help me handle this problem more systematically.

Thank you in advance for your support.

runing.mw