You write: "We see that P(u0,v0)=0."

I don't see that.  To get more help, upload your worksheet by clicking the big fat green arrow when you reply to this message.

@janhardo As you have noted, your code needs several corrections.  But even after those corrections a major impediment remains.  Your code intends to apply pdsolve,numeric to find w(x,y,t).  The problem that we face is that Maple's pdsolve,numeric is designed to solve PDEs in two independent variables.  So we are out of luck with solving for w(x,y,t).

Yet another major issue: After a few corrections, the PDE that you have attempted to present would describe the equation of motion of a membrane, not a plate which is the subject of this post.  The equation of the plate is of 4th order in the spatial variables.  See the equation included in my earlier answer.

In your description of the boundary conditions, you refer to the "clamped" boundary condition.  There is no such a thing as a clamped boundary condition for a membrane.  The clamped boundary condition applies to plates, and indicates that not only the displacement, but also the slope at the boundary is zero. 

@Scot Gould Your PDE problem is quite well-posed.  It's not your fault that Maple is returning the wrong solutions.  That's a Maple bug.  See the stripped-down example that I posted a few minutes ago that comes with an exact solution, while Maple gives the wrong answer.

So, for now, you need to solve your prolem in the old-fashioned way by hand.  Hopefully Maple's pdsolve will be corrected in future releases.

@dharr The heat equation with any type of Robin boundary condition is always well-posed.  Physical considerations do not enter the picture.  I suspect that your remarks stem from the unstated desire to have solutions that remain bounded in time.  But that's not a requirement for the solvability of a PDE.

The following example shows that the boundary conditions of the sort that was originally posed by Scott Gould is quite viable.  The solution is easily constructed by hand.  Maple 2024.1 returns the wrong solution.

Download robin.mw

@Gabriel Barcellos If your goal is to plot m versus T and G versus T, you don't need to calculate a sequence of points first.  You can plot them directly.  Here is how.

Download mw.mw

I was bothered by the fact that the simple answer, b=11, was obtained after combining some considerably large and messy expressions.  I looked and found a very simple solution that avoids the mess.  Maple is not of much help in this alternative approach, so I will just post my non-Maple calculation here.

@vv That's much better than my brute-force calculation, and also more correct in accounting for the order of tangency.  Vote up!

Your equation is y' = (1-x)*y^(-1).  That's the Benoulli equation with P(x)=0, Q(x)=1-x, n=-1.

@imparter 

There have been over 30 exchanges in this thread, and we are not yet close to obtaining the results that you are looking for. It seems to me that you are attempting to program in Maple at a level which is beyond your current state of knowledge. Perhaps you should set this project aside and focus on learning the basics of Maple programming, and then tackle this more advanced problem after gaining sufficient mastery of the basics.  Attempting to force your way through solving this particular problem is not a good way of learning Maple.

@imparter A few more errors fixed.  Pay closer attention to the details.

Query-Comments2.mw

@imparter In the attached worksheet I have pointed out a few issues that require your attention.  See if you can fixed those.

Query-Comments.mw

@imparter This worksheet handles the two sets of data through a for-loop.

Two_data-Fixed.mw

@imparter Upload your worksheet so that I may modify it.

@imparter I don't see a question in what you have written, so I can't tell what sort of response will be of help to you.  But for one thing, I see that you have not included the linestyle=dash in your code that I had suggested.  Did you try that?

@imparter The plot option linestyle=dash will plot with dashed lines.  Additionally, you may specify a list of colors for the graphs if you don't like the default colors.  So you may replace your current plot commands with

my_plot_1 := plot([%], r=0..h(z), color=["Red", "Green", "Blue", "Cyan"], linestyle=solid);
...
my_plot_2 := plot([%], r=0..h(z), color=["Red", "Green", "Blue", "Cyan"], linestyle=dash);

and then superimpose the two plots with

plots:-display(my_plot_1, my_plot_2);