Can one find an integral representation of the solution of the following system of PDEs?

pde1 := diff(f(x,y),x) + A(x) * ( p11* f(x,y) + p12 + p13*x ) 
= p14 * B(y)/B(x) * diff(f(x,y),x);

pde2 := diff(f(x,y),y) + A(y) * ( p21* f(x,y) + p22 + p23*y ) 
= p24 * B(x)/B(y) * diff(f(x,y),y);

f(x,y) is the unknown function,
A(x) and B(x) are known functions,
p11, p12, etc. are real parameters.

If p14=0 and p24=0, the right-hand...

Suppose N numbered cars start a race with starting positions N < ... < 4 < 3 < 2 < 1, car number 1 starting in front. (the car's index is the position on the starting grid) The race covers a total of L laps.

If two successive cars are in the position i < j, the probability that i overtakes j within 1 lap is P(i,j). This probability is independent of the position on the track and is constant throughout the race. For instance, if the starting positions...

Here is the sort of data I want to plot:

plot([seq([i,i],i=1..10),seq([i,1/i],i=1..10)],style=point);

The above works (Maple 14, Windows 7, Standard GUI). but I'd like to use different scales on the left- and right-hand sides, e.g. raise the second plot by a factor of 10.

I thought dualaxisplot would be the ticket, but I haven't been able to make it to work. It may have to do with the fact that my data is a list of coordinates rather than a function ...

I'm trying to reproduce the following graph:

http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/HarmonicNumbers.svg/600px-HarmonicNumbers.svg.png

I have got this far:

N:=10:
theHarmonicNumbersPlot := plot([seq([n,sum(1/i,i=1..n-1)-gamma],n=2..N)],style=point, colour=red):
theHarmonicFunctionPlot := plot(Psi(n), n=2..N, colour=black):
plots:-display([theHarmonicFunctionPlot,theHarmonicNumbersPlot]);

But my plot is missing the horizontal...

I have a vector consisting of taylor expansions of multiple variables, i.e. each element of the vector is a multivariate polynomial in X[1], X[2], etc. Not all the polynomials are of the same order, not all contain all the X[i]s.

I want to extract the coefficients of each component of the vector and store them in a Matrix.

I thought I had done it, but sadly the order of the coefficients is not what I expected.

Here is an example of a vector: