@mehdi jafari If you have initial conditions that make this system interesting, I'd be curious to see them.

@Carl Love The bug is fixed. Either download the code again, or simply change the exponent of -1 from j to k-j.

@mehdi jafari Thank you. There's a small bug in that code regarding the alternation of signs in computing the initial conditions. It'll probably take me a few minutes to fix.

By "normalize", do you mean that you want to rescale the amplitude to [-1, 1]?

Hint: What's equivalent to the remainder of p(x)/(x-a) for a polynomial p?

@Thomas Dean As I said above, it's documented at ?evalapply.

@Thomas Dean Yes, [f,g](a,b) becomes [f(a,b), g(a,b)]. It's as simple as that. In terms of a theory of operators, the function application operator distributes over the list-building operator.

I think that he means the syntax by which [cos,sin](t) becomes [cos(t),sin(t)]. If that's what you want, it's documented at ?evalapply, but there isn't much to say about it: It works that way, and that's it.

Another possibility is the prefix-form list constructor `[]`. 

@goli  The command textplot3d does not support any directional or rotational options, even in Maple 2020.

However, the colored-dots Answer below can be easily adapted to 3D plots, even in Maple 15.

@Carl Love I just posted a new Answer that doesn't use textplot.

@goli Sorry, there's no rotation option for textplot in Maple 15. This is a situation where you'll need a newer version.

I can concoct a solution that uses colored symbols (that are not arrowheads) to indicate the direction of travel.

@goli Did you re-execute the entire worksheet by clicking on the !!! on the toolbar?

@hym100 So, my solution is

C:= solve(int(c*x^2, x= 0..3)=1);
int(piecewise(x < 0, 0, x <= 3, C*x^2, 0), x= -1..1);
 

@goli Change the procedure Ang to

Ang:= tau->
    eval(
        eval(
            arctan(diff(y(t),t)*(Zmax-Zmin), diff(z(t),t)*(Ymax-Ymin)),
            sys11
        ),
        dsol(tau)
    )
:

I also recommend that you remove the stepsize option from DEplot and change the t-range to -3..3.

@goli I'll rewrite it to use plain eval. It should only take a few minutes.