@iman  I checked your statement.

See

Maple does not find this nontrivial solution.

Download 123456.mw

 Edited.

@Carl Love  I think the reason for the failure of OP is in using  vector  command instead of  Vector.

See:

X:=[seq(i^2, i=1..20)]:  # list 1

Y:=[seq(i^3, i=1..20)]:  # list 2

M:=vector(20, x->X[x]):

N:=vector(20, x->Y[x]):

plot(M,N); 

Good morning  Alsu! I am very pleased to see the new user from Russia in this  forum. I live right next to you in the city of Penza.

Here are some tips to improve your codes:

1. To create simple animations to be more efficient use of  plots[animate]  command, in which the frames are generated automatically:

restart;

plots[animate](plot, [[x,y, y=-20..20], linestyle=2, color=red, thickness=4], x=-10..10, frames=60);

2. I do not understand why you use plots[implicitplot] command (instead of plot command) in your further examples  transformations of simple plots defined by explicit formulas. Using a list, you can create multiple plots in one coordinate system:

restart;

plot([sin(x), sin(3*x), sin(1/3*x)], x=-3*Pi..3*Pi, y=-1.4..1.4, color=[red,blue,green], linestyle=[2,1,1], thickness=[2,3,3], scaling=constrained, legend=[typeset("  График функции  ", y=sin(x)), typeset("   График функции  ", y=sin(3*x)), typeset("  График функции  ", y=sin(1/3*x))], legendstyle=[font=[times,roman,14]]);

3. To work with the objects, depending on the parameters,  Explore command is very helpful. See help for details on this command.

@adel-00  To avoid this, it is impossible - this is the nature of the solutions to this equation. To find a solution further right of  1.5355176  you need to set new initial conditions, for example

restart:

with(plots):

ini1:=D(x)(1.54)=0, x(1.54)=1:

dsys:=diff(x(t),t,t)+(x(t)-2)*diff(x(t),t)+5*x(t)=0;

dsol1 :=dsolve({dsys,ini1}, numeric, abserr=1e-9, relerr=1e-8, maxfun=0);

plots:-odeplot(dsol1, [t,x(t)], t=1.54..4, axes=boxed, color=black, linestyle=1, tickmarks=[6, 6], axes=boxed, titlefont=[SYMBOL,12]);

We see that there is a new singularity  3.0755176, about which the plot goes to minus infinity.

@acer  Thank you for the correction. It was my carelessness when typing of the code.

@Markiyan Hirnyk  Perhaps the reason for this in the operating system. I have Windows 8.1

@Markiyan Hirnyk   On my comp in Maple 2016.1  I see:

plot3d(x^2-y^2, x = -1 .. 1, y = -1 .. 1, axes = normal, style = surfacewireframe);

@Markiyan Hirnyk  Edges, already passed, are marked in red:

with(GraphTheory):

G := Graph(Trail(1, 2, 3, 4, 5, 6, 4, 7, 8, 2));

L := RandomWalkOnGraph(G, 2, 20);

n := nops(L):

for i to n do

HighlightVertex(G, L[i]);

if i >= 2 then HighlightTrail(G, L[1 .. i]) end if;

M[i] := DrawGraph(G);

G := Graph(Trail(1, 2, 3, 4, 5, 6, 4, 7, 8, 2))

end do:

plots[display](seq(M[i]$10, i = 1 .. n), insequence = true);

with(GraphTheory):

G := Graph(Trail(1,2,3,4,5,6,4,7,8,2) );

L:=RandomWalkOnGraph(G,2,20);

for i in L do

HighlightVertex(G,i);

M[i]:=DrawGraph(G);

G := Graph(Trail(1,2,3,4,5,6,4,7,8,2) );

od:

plots[display](seq(M[i]$10,i=L), insequence=true);

@Markiyan Hirnyk  Thank you. As for the animation, it is very easy to do, if you use  HighlightVertex  command. But now I have no time to do it, because half an hour begins the final of the European Football League.

@Carl Love   Many thanks for the work done to improve my procedure. Convert your comment to an answer  that I was able to vote for it. It will also be helpful if you added your version as a comment to my post.

@farazhedayati  Unfortunately in the procedure provided that the variables have the names  x  and  y . I replaced the variable  a  with  y . Now it works:

PP := subs(a = y, 0.3800179925e-3*exp(-0.6065722618e-3*(x-29.51704536)^2+(0.6650093594e-3*(x-29.51704536))*(a-12.94061928)-0.1106850312e-2*(a-12.94061928)^2));

ContoursWithLabels(PP, -20 .. 20, -20 .. 20, {seq(0.1e-3 .. 0.3e-3, 0.5e-4)}, [color = black, axes = box], Coloring = [colorstyle = HUE, colorscheme = ["Cyan", "Red"], style = surface]);

@Markiyan Hirnyk  A similar incorrect plotting:

plot(1/x, x=-5..5, y=-5..5, color=red, thickness=4);

@Markiyan Hirnyk  You have incorrectly wrote the first equation (see the original post). Here are the individual plots of the first and second equations. It is clearly seen that the first set (for y<>0) is a subset of the second set. This is a graphic illustration of what I wrote earlier:

a:=sin(165*Pi/180-theta)/10-sin(theta)/y:

b:=(((y^2-20*y*cos(Pi/12)+100)*(sin((165*Pi/180)-theta))^2)/100)-sin(Pi/12)^2:

plots:-implicitplot(a, y=-10..25, theta=0..2*Pi, gridrefine=3, thickness=2):

plots:-implicitplot(b, y=-10..25, theta=0..2*Pi, gridrefine=3, thickness=2):

plots[display](<%% | %>);

@spalinowy  I do not understand what your problem. Please download the Maple worksheet in which you received the wrong matrices.