Improved FastPursuit2 procedure

FastPursuit2(5, 1.5, 1.0, 0, 2.0, 0., 1200, 0.05) example: the wolf is running in a almost concentric circle at almost fixed distant (not this plot)

achtervolgings_kromme_wolf_en_geit_mprimes_DEF_14-9-2025_.mw

achtervolgings_kromme_wolf_en_geit_mprimes_14-9-2025_.mw

Making now a FastPursuit2  procedure using dsolve :
sol := dsolve(sys union ics, {xw(t), yw(t)}, numeric, method = rkf45)

@Alfred_F 
 

Starting position and speed are decisive?

The goat continues to move in a circle

The wolf remains focused on the goat

Was it not with a pursuit curve?

Bring back  the number of sliders ? 

@Alfred_F 
Yes, that is a proof by contradiction, looks like on the proof voor the irrationality of square root two number
aside:
The ancient Greeks were confronted with the existence of the square root of 2 and believe that it came as a shock to their world view at that time.

periodiciteit_cos_achtergronden_mprimes7-9-2025.mw

@vv 
In my opinion, this is a mathematical proof sketch and the correct details should be filled in.
Getting this expression for cos(2pi.n) seems to be straight forwards ?, but now further..?

@Carl Love 

@Alfred_F 
niet_periodieke_functie_-mprimes_6-9-2025.mw

Was @Alfred not reffering to the function  exp(x) ?
bewijs_perodiciteit_mprimes_4-9-2025.mw
y=cos(x) is not bijective 

I can enlarge screen in windows 11 pro  with Ctrl + Middle mouse wheel ?

@Alfred_F 
This is userfriendlier by using y(x) explicit 

Download ode_via_odesteps_mprimes24-8-2025.mw

The dependent variable cannot be easily isolated. ?

If b= 0 in ic y(0)=0

y1 := sqrt(2*x);
y2 := sqrt(2*0.5*x);
y3 := sqrt(2*(-1)*x);
p1 := plot(y1, x = 0 .. 5, color = red, thickness = 2, legend = "a = 1");
p2 := plot(y2, x = 0 .. 5, color = green, thickness = 2, legend = "a = 0.5");
p3 := plot(y3, x = -5 .. 0, color = blue, thickness = 2, legend = "a = -1");
display([p1, p2, p3], title = "Solutions of y(x) = sqrt(2*a*x) with Initial Condition y(0) = 0", labels = ["x", "y(x)"], axes = boxed);

@salim-barzani 
I don't think I fully understand you.

@salim-barzani 

Do you want to calculate all this manually?

Then you need to extract the procedures from the wkptest module.

The procedures must be reduced from general to a single calculation.