@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.

Can Maple give a another answer than this ?
sin^2(a)+cos^2(a) =1 
sin^2(a)+cos^2(a) +1 = 2 
sin^2(a)+1 = - cos^2(a) +2  
Pythagoras in the unit circle.

@salim-barzani 
Don't invent the wheel again...lol
a12_interactieparameter_2_soliton_mprimes13-8-2025.mw
 

@acer 
Thank you, don't make the calculation bigger, but more efficient.

That's what I understand from it.

@acer 
I can't manage to create such a nice short procedure like you do. 

splitsen_in_lineair_en_niet_linear_werkend_def_CORR2procedure-12-8-2025.mw

@acer 
Would it be correct to say that t and K are degree 1 and a number is degree 0  and both lineair ?
linpred (graad 0 óf 1 ⇒ “lineair”)  

splitsen_in_lineair_en_niet_linear_werkend_def_CORR1_12-8-2025.mw

@salim-barzani 

splitsen_in_lineair_en_niet_linear_werkend_def_12-8-2025.mw

@salim-barzani 

For a pde you can select lineair en not llinear terms by hand 

L := convert(expand(pde1), list, `+`)
lineair := L[1] + L[2]

A procedure , numeric, symbolic sphere equation for given sphere centre and 3 circles 

A phytagoras circles example

res := SphereFromSections([8, 4, 0], 4, 3, 5, symbolic = true, plot = true);
res[equation];
res[center], res[radius];

"Sphere equation: ", (x - 3.000000000)^2 + (y - 4.000000000)^2 + z^2 = 25.00000000

opgave_rouben_bol_mprimes_procedure_nmeriek_en_symbolisch_11--8-2025DEF.mw

@Rouben Rostamian  
Ai says  , its ill posed?
At first, the Ai said that the task was impossible, but later AI said that it was possible.( again question) 

.

Download opgac_rouben_bol_mprimes_11--8-2025.mw

@sand15 
The ai  is improved lately, and seems to be much better , making this is not a achievement
bolvergelijking_opstellen_mprimes_10-8-2025.mw

@Carl Love 

bolmet_punt_mprimesDEF_10-8-2025.mw