@acer 

Hello

Can you explain,what is number 5 and 50 in this code below:

{guard::posint:=5,maxtries::posint:=50}

Thanks.

@tschuermann 

I attached MMA notebook if it's useful to you:HeunC.zip

@vv 

What is the correct answer, because I'm not sure of my answer for OP ?

@Markiyan Hirnyk 

MMA  11.3 says:

Is Mark Viola is wrong with his answer. It has 127K reputation?

What is the source of this plot? References ?

Only workaround.Convert to abs or signum(strange two white lines !) also works.

f := max(1, min(x, 2))+max(1, min(y, 2));

f2 := convert(op(1, f), piecewise)+convert(op(2, f), piecewise);

plots:-inequal(f2 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

f3 := convert(op(1, f), abs)+convert(op(2, f), abs);

plots:-inequal(f3 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

f4 := convert(op(1, f), signum)+convert(op(2, f), signum);

plots:-inequal(f4 <= 3, x = -5 .. 5, y = -5 .. 5, 'nolines');

Why you Not gives thumbs-up(votes) for correct(good) answers ?
I think you should give an award for someone else's for hard work?

List question No Votes by you:

1.Comparison of coefficient of exponential function

2.Problem to comapre to coefficient

3.Want to write an expression in sigma notation

4.Problem in transpose of matrix

5.Problem in 2D plotting

6.Need roots of cubic equation

7.Problem in integrating an expression

8.Define axis for 2D plotting

9.Problem in summation

10.Generate a matrix and block matrix

11.Problem to find integration

12.Problem to simplify an expression

13.Want expression in on bracket

14.:Problem in elimination

15.Draw a set of points in 3D and want surface style

and more...

@Markiyan Hirnyk 

(* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" *)
    
    sol = Reduce[{4*x1 + 7*x2 + 6*x3 == 186, 
    Floor[(1/2)*x1] + Floor[(1/5)*x2] + Floor[(1/3)*x3] == 18, 
    Floor[(1/5)*x1] + Floor[(1/2)*x2] + Floor[(1/4)*x3] == 21}, {x1, 
    x2, x3}, Reals];
RegionPlot3D[ImplicitRegion[sol, {x1, x2, x3}], MaxRecursion -> 2, PlotPoints -> 10](* ? *)

Gives a empty plot. Maybe user  vv 4397 is right.

2D version:

eq2 = {Floor[(1/2)*x1] + Floor[(1/5)*x2] + 
     Floor[-(2/9)*x1 - (7/18)*x2 + 1/3] - 8 == 0, 
   Floor[(1/5)*x1] + Floor[(1/2)*x2] + 
     Floor[-(1/6)*x1 - (7/24)*x2 + 3/4] - 14 == 0};
sol2 = Reduce[eq2, {x1, x2}, Reals]

RegionPlot[ImplicitRegion[sol2, {x1, x2}]](*Warning !!! MMA eat's RAM Memory. A bug ? *)

RegionPlot[ImplicitRegion[sol2, {x1, x2}], 
 Method -> {"DiscretizationMethod" -> "Symbolic"}, MaxRecursion -> 2, 
 PlotPoints -> 10](*Workaround*)

@VMorsaint 

Extract real solution using remove command witch user Acer mentioned:

sol := [RootFinding:-Analytic(4^x+1-x^4, x, re = -5 .. 10, im = -2 .. 2)]: remove(is, sol, nonreal);

#[2.09401285285812, -1.05356701067272, 3.98972895158790]

Answer looks better if you use  LogicalExpand.

sol = Reduce[{4*x1 + 7*x2 + 6*x3 == 186, 
   Floor[(1/2)*x1] + Floor[(1/5)*x2] + Floor[(1/3)*x3] == 18, 
   Floor[(1/5)*x1] + Floor[(1/2)*x2] + Floor[(1/4)*x3] == 21}, {x1, 
   x2, x3}, Reals] // LogicalExpand

RegionPlot3D[ImplicitRegion[sol, {x1, x2, x3}]]

@Carl Love 

Thanks for showing Maple weakness in: inttrans(fourier(piecewise function)).

I need convert twice piecewise function :P

@Preben Alsholm 

Nothing new,Maple leaks  like a sieve.Thanks for info.

@Preben Alsholm 

Thank you for quick fix.  :)

@isifesai 

Code for Maple below 2018 version.

Integro-Eq_Ver_3A.mw

@panke

I edited my answer and works as it should.