Not necessarily (almost any numerical method can be fooled), but it's a possibility to consider seriously.

Not necessarily (almost any numerical method can be fooled), but it's a possibility to consider seriously.

It looks to me like there may be no real solutions.  At least, fsolve can't find any.  Do you have reason to think there are solutions?  If so, can you give ballpark estimates for the variable values in such a solution?

It looks to me like there may be no real solutions.  At least, fsolve can't find any.  Do you have reason to think there are solutions?  If so, can you give ballpark estimates for the variable values in such a solution?

Well, you didn't tell it to take those results.

Try this:

> F:= s -> subs(sol1(s),(exp(.5e-1*t)*(-.5e-2*(W(t)+98400-R(t))^2-(410*(W(t)+98400-R(t)))
    *exp(.5e-2*t)-W(t)*(1070-.22*H(t)+.1e-4*W(t))-R(t)*(336+.85e-3*R(t)))));

> evalf(Int(F, 0..40));

-.2005670456e11

Well, you didn't tell it to take those results.

Try this:

> F:= s -> subs(sol1(s),(exp(.5e-1*t)*(-.5e-2*(W(t)+98400-R(t))^2-(410*(W(t)+98400-R(t)))
    *exp(.5e-2*t)-W(t)*(1070-.22*H(t)+.1e-4*W(t))-R(t)*(336+.85e-3*R(t)))));

> evalf(Int(F, 0..40));

-.2005670456e11

Why don't you try following the instructions?  Start by writing middlesquare.

Why don't you try following the instructions?  Start by writing middlesquare.

What triangles?  Do you mean the > prompts?  To turn them off, try

interface(prompt="");

(or use Document mode)

What triangles?  Do you mean the > prompts?  To turn them off, try

interface(prompt="");

(or use Document mode)

If you take the equations literally, there are no solutions, as I said. 

"Now you say that qd is undefined when xd=0: is that all there is to it? From that, can we conclude that there is no triplet (x,c,q) that makes {xd=0, cd=0, qd=0} true ?"

Yes, that is it.

However, since you can write qd *xd = (q-1/50)*(3/100-q)*xd +(q-1/40)*cd (when xd <> 0), the surface (q-1/50)*(3/100-q)*xd +(q-1/40)*cd = 0 consists of the surface qd=0 plus the curves where xd = 0 and cd = 0 intersect and the curves where xd=0 and q=1/40 intersect.  So a plot will appear to show xd = 0, cd = 0 and qd = 0 all intersecting on the following curves:

> solve({xd = 0, cd = 0});

{c = x^(1/2)-1/10*x, q = -1/10*(-5+x^(1/2))/x^(1/2), x = x}, {c = 0, q = q, x = 100}

 The Maple tag is acting up again: this last one should be {c = 0, q = q, x = 100}.

Again, it's not clear to me what you're really hoping to find. 

There is literally no such thing as a solution of {xd, cd, qd}, because qd is undefined when xd = 0.  No amount of graphing will change that.
For any positive x, {c = sqrt(x)-1/10*x, q = 1/(2*sqrt(x)) - 1/10} gives you xd = 0, cd = 0 and qd undefined.  That is approximately true for the solution you got from fsolve, but there's nothing particularly special about this solution.  As for the limit of the indeterminate form cd/xd as you approach this solution, that will depend on the path you're using to approach the solution.  In my previous posting I took a limit with c and d fixed and x changing.  But if you took x and q fixed with q = 1/(2*sqrt(x)) - 1/10 and c changing, you'd have cd=0 so the limit would be 0.  Or if you took some other path, you would get some other limit.   In fact, you could get any limit you want, or no limit at all, by choosing the path properly.

This requires the Standard GUI.  I have tested it in Maple 12: it will probably work in 11, maybe also in 10, but certainly wouldn't in anything before 10.

This requires the Standard GUI.  I have tested it in Maple 12: it will probably work in 11, maybe also in 10, but certainly wouldn't in anything before 10.

plot(x^k, x=-1 .. 1, title = sprintf("The plot for value %d",k));

or even (when using Standard GUI)

plot(x^k, x=-1 .. 1, title = typeset("The plot of ",x^k));