@Rouben Rostamian   It is not important, but where/how did you choose the location and names for black labels "x" and "y" in your nice picture?

@Preben Alsholm 

Because when I'm trying to copy it here from Maple, some error report saying "cannot copy and paste is unavailable in Firefox and Mozilla" occurs :-(

However, I've just used what I wrote above with

d

----

d q2

notation.

The notation is selfexplanatory, but does not work. I think that Maple expects some other format of the ODE.

I just wanna differentiate the r.h.s. of this:

u_2(q1,q2)=q2*p(q1+q2)-c2(q2)

along q2,substitute r2(q1) for q2 and put it equal to 0, and obtain (=solve for) r2 which should be for the given

c2 and p (these 2 functions are known and given above), equal to (1-q1-c)/2.

And all this with Maple!

Yes,it works.What is the difference between add and sum?Thanks

But why Maple cannot give a CLOSED FORM for this recurrence?

Ok, this is a code. What if I'd like a closed formula with variables k and n in it?

This is just my typo. Of course let M(0,0) be 0 and add any bounadries necessary.

The actual problem is that Maple solves only for ONE variable :-(