odeplot allows you to plot multiple plots on the same graph.

with(plots): p1:=plot([(x/(2*sqrt(x)-3)),(-x+5)],x=-10..10,y=-4..6,discont=true, linestyle=[1,3],color=[red,navy], thickness=2): p2:=textplot([[7,1,"nice blue line"],[7,5,"nice red line"]]): display(p1,p2);

I might try to generate random Hermitians RandomMatrix(4,4,generator=0..1.0,outputoptions=[shape=hermitian]); Then find the minimum eigenvalue. If it is negative, create a DiagonalMatrix with the negative of the min ev as diagonal entries and add it to the original. This pushes the eigenvalues up so the smallest is zero, so then you have a positive semidefinite matrix. Probably you want definite or semidefinite, so you could add a random number to the diagnonal entries to push then up further. Then scale the matrix so the trace is 1. This isn't perfectly random I suppose, but maybe it's OK for your application.

An example of something like this is below (I assume you mean spherical co-ordinates). Note the colour function does some automatic scaling. The axes are hardest, since by default they are cartesian. I think you would have to generate the legend separately. plot3d(phi*cos(phi)^3,theta=0..2*Pi,phi=0..Pi/2, coords=spherical,scaling=constrained,color=phi,style=patchnogrid,axes=normal);

Here it is for xi=x3; fairly easy to generalize.

> y:=x3*(a-(x1+x2+x3+x4+x5)-b);

> dydx3:=diff(y,x3);

> solve(dydx3=0,x3);

>

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you could try to change variables so that x=infinity is at a finite value. E.g. u=1-exp(-x) has u=0 at x=0 and u=1 at x=infinity. The d.e. then becomes I think f'(u)*(1-u)+f(u)*f''(u)=0 and you could then do the same for the boundary conditions.

With more eqns than variables it is likely that there is no solution. But in any case, I find that once Maple starts to use virtual memory on disk (with the symptoms you mention) it's a waste of time proceeding.

Your r.r needs to be r(t).r(t) to get the expression you want. But there is still a problem since this is a scalar and you are adding it to a vector. You can't differentiate a vector like this; you need to code your problem as three separate differential equations.