@Thomas Richard 

Here is an example when "capturing" this information could be useful.
Suppose you have a file foo.mw which contains the definition of a module named foo  and a command 

savelib(foo, "foo.mla"); 

You execute the worksheet foo.mw at date T.
How can you be 100% sure that the foo.mla you use at date T' > T has been created from the foo.mw that existed at time T?
To  answer this question I decided years ago to "programatically capture" the name of the worksheet foo.mw within this procedure, its modifaction (through FileTools) and the name of the operator (ssystem("whoami")) and augment the archive foo.mla  with the informations.

 Taches  := ssystem("tasklist /V /FO ""LIST"" "):
 MaTache := StringTools:-StringSplit(Taches[2], "javaw.exe")[2]:
 MaTache := StringTools:-StringSplit(%, "Maple 2019")[1]:
 MaTache := StringTools:-Squeeze(MaTache):
 MaTache := StringTools:-StringSplit(MaTache, "fenˆtre: ")[2]:
 MyWS    := StringTools:-StringSplit(MaTache, "*")[1]:
 MyWS    := StringTools:-SubstituteAll(MyWS, "\\", "/"):
 WSepoch := FileTools[ModificationTime](MyWS):

 Seed  := randomize():
 GenID := StringTools:-Random(20, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"):
 INFO := table([
     "CreationDate"       = StringTools[FormatTime]("%Y.%m.%d_%H.%M.%S"),
     "WorksheetName"      = MyWS,
     "WorksheetEpochTime" = WSepoch,
     "Author"             = op(-1, ssystem("whoami"))
 ]):

 LibraryTools:-Save(INFO, "foo.mla"):

By the time I couldn't find any versioning tools that were secure enough to guarantee the link between  foo.mw and foo.mla.

The weak link in my strategy is that you heve to save foo.mw before executing it and thus creating foo.mla.

@acer 

Very nice solution, I vote up!

I was working on a solution based upon RegSub/RegSubs.
Both of these functions seem very powerful but I find their help pages somewhat obscure.
Could you give me some hints on how they work?

TIA

@dharr 

Hi,
You're right, the qolution is OS-dependent.
For instance, for years I use the trick I explain in my answer to @mjc .

A priori, an equivalent strategy could be based on this command if you use a Linux machine, but I never checked this.

xprop -id $(xprop -root -f _NET_ACTIVE_WINDOW 0x " \$0\\n" _NET_ACTIVE_WINDOW | awk "{print \$2}")

The thing is it doesn't work on Mac OSX (_NET_ACTIVE_WINDOW is unedfined) and I never found out how to reproduce with Mac OSX what I do with Windows (no clear equivalent to tasklist).

Maybe this can give you some ideas if you want to go further

@tomleslie 

Thanks for your reply.
At least this shows that there is no version issue.

@tomleslie 

"and there is probably not much you can do about it!"
You're wrong, simply the resolution of hyperbolic pde requires a minimum of precautions.
I invite you to consult my answer.

Nevertheless, I do acknowledge that there may be a version problem (2015 = 2020 <> yours).

@Athar Kharal 

See my answer from my home login @mmcdara.
When I was at the office (@sand15) I used Maple 2020 and it worked just fine (like Maple 2015 if I'm not mistaken).

@aimLow 

It's a matter of point of view and probably of usage. and historical conventions.

Take the Boyle-Mariotte's law for perfect gases.
It came from observation that, keeping T constant, the measures (v, p) was closely aligned on an hyperbola branch, thus suggesting that p was of the form p=Constant/v.
But this relation is mostly written p*v = constant.

On the other side one keeps writitng P*v = n*R*T and not (as I said in my answer f(p, v, T) = 0) p*V-n*R*T = 0.

IMO, something like f(p, v, T) is less confusing and more general when we cannot isolate one thermodynamical quantity in terms of the two others.


Here is a (maybe) more formal way to do what you askd for:
 

Download WanDerWalls_eos_2.mw

@ajahyaya

To complete @Rouben Rostamian  advice:

sys := eval({eqn1, eqn2, eqn3, eqn4, i(0) = 11437, r(0) = 1077, s(0) = 1770000, t(0) = 1087}), {i(t), r(t), s(t), t(t)}:

print~(sys):

will present each equation and initial condition on a different line to ease the visual analysis.

Also useful when womething goes wrong, is to check if the functions which appear in "diff" are also the functions which appear in initial or boundary conditions:

# functions you take derivatives
dfn := select(has, indets(sys, function), diff):
dfn := map2(op, 0, map2(op, 1, dfn));

# functions you define initial conditions for
fn0 := map2(op, 0, lhs~(ic));

Finally, check for all possibly non numerical parameters.
In your initial worksheet:

sys := {eqn1, eqn2, eqn3, eqn4, i(0) = 11437, r(0) = 1077, s(0) = 1770000, t(0) = 1087}:

# independent variable (t)
indepvar := op(2, select(has, indets(sys, function), diff)[1]);
                               t

# remaining parameters
indets(sys, name) minus {indepvar}
                            {T, mu}

Here you have two formal parameters (using print~(sys) reveals mu has not been set to 0.04 as intended).
As @Rouben Rostamian said it is unsafe to use mu and mu[1]; look at this

restart:
mu    := 2;
mu[1] := 3;

                               2
                               3
mu, mu[1];
                             mu, 3
restart:
mu[1] := 3;
mu := 2;
                               3
                               2
mu, mu[1];
                            2, 2[1]

Two possibilities to avoid this issue:

restart:
mu[0] := 2:
mu[1] := 3:
'mu[0]' = mu[0], 'mu[1]' = mu[1];

                      mu[0] = 2, mu[1] = 3
lprint('mu[1]');
mu[1]


restart:
mu := 2:
mu__1:= 3:
'mu' = mu, 'mu__1' = mu__1;

                       mu = 2, mu__1 = 3
lprint('mu__1');
mu__1

A last point, in case you really don't want to set T to some numerical value you can do this

dsn := dsolve(sys, numeric, parameters=[T]):

# Specialize dsn for some value of T
dsn(parameters=[1]):

# Plot as usual
plots:-odeplot(dsn, ....)

One advantage of keepping free some parameters can be seen here:

restart:

dsn := dsolve({diff(x(t), t)=a, x(0)=0}, numeric, parameters=[a]):

# Compare the solution for different values of T
p := NULL:
for tau from 1 to 3 do
  dsn(parameters=[tau]):
  p := p, plots:-odeplot(dsn, [t, x(t)], t=0..1, linestyle=tau)
end do:
plots:-display(p);

@dharr 

Thanks,
one of my rare moments of inspiration

There are already many questions and answers about the SIR model.
Maybe you could start by looking at them, maybe you will find something interesting
https://www.mapleprimes.com/search/postsandquestions?term=SIR

In any case, it would be better if you would post your worksheet using the big green up arrow in the menu bar.

See you soon

@ecterrab 

Wonderful explanation (even though I still need to delve deeper into your answer to fully understand it).
As a numerical and data analyst I'm much more familiar with the the numerical aspects of ODEs. You have opened up a world for me.

Great thanks

@ecterrab 

Hi, 
Di you have any idea why dpolyform fails to find an ODE that g(x) verifies

e := g(x) = 1/(1+x):
PDEtools:-dpolyform(e, no_Fn);
      [g(x) = 1/(1+x)] &where []

as it is obvious that 

diff(g(x), x) = -g(x)^2:

TIA

@sursumCorda 

Sure. The only difficulty is that minimizing the sum of orthogonal distances (named "Orthogonal Regression") is no longer a linear problem and and one has to use an optimization procedure.

BTW, here is a very educative application whcich visually explains what ordinary least squares regression is :
  Start > StatisticsAndProbability > Least Squares Approximation

Please load your worksheet by using the big green arrow in the menubar

@rlopez 

I like the geometry package for the elegant way it can solve a problem, but I have to admit that your solution is even nicer (although of black box type).
I vote up