A phase-plane plot makes sense for autonomous differential equations, that is, differential equation whose coefficients do not depend on time.  The cos(wt) term makes your equation nonautonomous.  A phase-plane plot, even if you manage to produce one, conveys no useful information.  You should rethink your question.

Preben, I an unable to execute this code.  I run into an error in computing J1a.  I am puzzled, because the error is due to the Change(J1,s=-t) which seems to be rather innocuous.  I have attached a worksheet to show what I am getting.

mw.mw

Rather than replying individually, I want to issue this collective Thank You for the very insightful solutions and comments from which I have learned quite a bit.

A car's forward acceleration is produced through its engine, which uses fuel  The reverse acceleratiom is produced by the breaks, which use no fuel.  Your formula for the energy consumption, that is integral F_acc(s) ds, should be changed to

int(max(0,F_acc(s)), s=0..d);

That corrects the problem's formulation.  I haven't thought about its solution.

@ The help page for "fsolve,details" recommends specifying an interval with fsolve.  Thus, we do:

sys := {6*exp(x+y)/(1+exp(x+y))+exp(2*y)/(1+exp(2*y)) = 2,
            5*exp(2*x)/(1+exp(2*x))+2*exp(x+y)/(1+exp(x+y)) = 1};
fsolve(sys, {x=-2..0,y=-1..1});

and we get

I suppose that you expect the solution to be x = 2*A - 5.

Now, you tell me, what does it mean to subtract a number from a vector?

What equation are you trying to solve?

@erik10  Let's say we replace the first equation by:

0.44 - a < PA^2 + 2*PA*PB < 0.44 + a

where "a" is the known absolute error in the 0.44 value.  We replace the remaining equations in a similar way.  Furthermore, since PA, PB, and PO are probabilities, they should be between 0 and 1.  Thus, your problem amounts to solving a set of 14 nonlinear inequalities in the three unknows PA, PB, PO.

I think this is a nonlinear optimization problem.  Unfortunately I don't know much about the subject to offer you some help here.  Perhaps others who know more can comment.

@Preben Alsholm 

a/x^b produces a pretty good fit:

q:=Statistics:-Fit(a/x^b,data,x);

@hhoang1 OK, then. Consider:

Plug in x=3.  What is the value of y?

Do it on paper, not Maple!

Does this throw some light on the problem?

@hhoang1 That depends on where you put the missing parenthesis.

1. The mathematical expression that you have shown has four opening parentheses and three closing parentheses.  Needs to be fixed.
2. You forgot to say over which range of x values you need to plot.

@Klockjj Now the problem is in ode3 which, in a skeleton form, looks like

diff(P(z),z) = -1/P(z);

Solving this with P(0)=1 we get:

P(z) = sqrt(1 - 2*z);

Therefore the solution cannot extend beyond z=1/2 in this case.  Essentially the same thing is happening with your more complex equations.  It's time to go back and examine the derivation of the model.

@Bendesarts I have often wished that the whole worksheet would act as the Code Edit Region does, but so far as I know that's not possible in the current implementation.

Actually there may be fundamental obstacles in autoindenting a whole worksheet.  A Maple worksheet is conceived as an interactive interpreter of Maple code.  You can type a code fragment here, another code fragment there, and one gets interpreted and executed independently of the other.  To autoindent an entire worksheet, the indentation of each part would be affected by all other junk that may exist in the worksheet and probably that's not what you would want.

The Code Edit Region isolates a chunk of the worksheet from the arbitrariness of the rest of the worksheet and which gets autoindented as best as possible.

I don't use the Code Edit Region myself.  That's because autoindenting within a Code Edit Region is only partially implemented -- the code gets indented to the right properly, but leftward indentations needs to be done manually.  I also wish that there were an option to re-indent a code region whose indentation was messed up through multiple editings.

If a time comes when full autoindening is implemented in the Code Edit Region, I may consider using it.

@sarra The attached worksheet shows how to calculate and simplify the product x &x y.

It also shows how to calculate f(x &x y) and partially simplify it but the simplification in this case is incomplete.  Perhaps someone here more knowledgeable about Maple can show you how to complete it.

Note: I typed the entire worksheet from scratch.  I may have made errors in transcribing your formulas.  Be sure to check for correctness.

mw.mw