Do not remove the original question. Instead create a new question.

Do not remove the original question! Make a new question instead.

Please don't edit out the question! People refer to these questions and answers for years to come. If you edit out the question, they can't. So please put it back.

@Markiyan Hirnyk I'll remember that sacred cow saying. Another saying is "The perfect is the enemy of the good."

One vote up is mine.

@J4James This system is very close to the extensively studied Lorenz system. Indeed, it is so close that I think that the OP made a typo. The only difference in the Lorenz system is that the second equation has 28-z(t) where the OP has 28-x(t).

@mohammad2232 The command implicitdiff(..., y, x, x) produces the second derivative of y with respect to x (d^2y/dx^2). The notation (-cos(t)/sin(t))' indicates the derivative with respect to t of the derivative of y with respect to x. In differential notation it would be (d/dt) (dy/dx) or perhaps d^2y/dx/dt. To get d^2y/dx^2, you need to divide this by dx/dt, or just let implicitdiff do it all as one computation.

@Carl Love Axel's method of changing the numeric integration method is much faster than mine.

@PunkRediska Your expressions are too long for me to cut-and-paste. Would you please upload a worksheet with the definitions of the four variables Vx, Vy, xxx, yyy? The worksheet doesn't need to have anything else, if that helps.

A quick glance indicates to me that your functions have an extreme number of points of non-differentiability.

To get any help, you'll need to post the code for your preliminary steps such as Vx, Vy, xxx, and yyy.

@Arka The expression can't be factored other than factoring out the constant 16. You can easily prove that (pp1^2+pp2^2+pp3^2) is not a factor by evaluating a at integer values for all the variables and then checking whether the result is divisible by (pp1^2+pp2^2+pp3^2):

A:= eval(a, [Q1=3, Q2=5, Q3=7, Q4= 11, pp1= 13, pp2= 17, pp3= 19]);
                          53328924928
P:= eval(pp1^2+pp2^2+pp3^2, [pp1= 13, pp2= 17, pp3= 19]);
                              819
A/P;
                          53328924928
                          -----------
                              819    

@Arka Then the expression is not factorable as entered. Since you posted your expression as an image rather than as plaintext, I cannot work with it.

@Markiyan Hirnyk What is your point? The options numpoints and gridrefine are not mutally exclusive; options numpoints and grid are. Option numpoints determines the initial grid.

@Carl Love Continuing from above, arbitrarily select omega = 12, so omega^(-1) = 17. Then the matrix DFT is

DFT:= Matrix(4,4, (i,j)-> 12^(i*j) mod 29);

and the inverse transform matrix is

IDFT:= Matrix(4,4, (i,j)-> 17^(i*j) mod 29);

You can verify that their product is 4I by

DFT.IDFT mod 29;

@abbeykabir Sorry, I can't think of any reasonable way to plot a parametric curve over the complex numbers. If it were possible to express it as y = f(x), then there are some possibilities. But that is not possible for this x and y.

@sunit Ah, I see. Was the restart in the .m files? Then that's the problem. The restart only works at the top level, not in a file, and it should be placed in its own execution group.