restart;

Do you know why this plot is not complete (cut from -infinity to minus 2)? In Mathematica I haven't got that problem so I wonder what is wrong here.

with(plots);
plot((x^3 - 4*x^2 - 9*x + 36)/(x^3 - 9*x), color = red, discont = true, view = [-3 .. 3, -5 .. 5]);

Hi!

Do you know why the sequence of output is difference than the handing output?

restart;
a := 1.4;
b := 0.3;
x[0] := 1;
y[0] := 1;
<x[n + 1], y[n + 1]> = <b*y[n] - x[n]^2 + a, x[n]>;

f := (n, m) -> (-n^2 + b*m + a, n);
 

g := (k, n, m) -> (f@@k)(n, m);

seq([g(a, x[0], y[0])], a = 0 .. 3);
        [1, 1], [0.3, 1], [0.61, 1.3], [-0.2701, -1.99]

[g(0, x[0], y[0])], [g(1, x[0], y[0])], [g(2, x[0], y[0])], [g(3, x[0], y[0])];
        [1, 1], [0.7, 1], [1.21, 0.7], [0.1459, 1.21]

Hi! Do you know how can we make more transparent code for this animation plot? I want something similar to this but only for one spot:

my code:

restart;
with(plots);
with(plottools);
display(plot([cos(x), sin(2*x), x = 0 .. 2*Pi]), animate(pointplot, [[[cos(a), 0], [0, sin(2*a)], [cos(a), sin(2*a)]], color = [red, green, green], symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), 0], [cos(a), sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[0, sin(2*a)], [cos(a), sin(2*a)]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), implicitplot(x = cos(t), x = -1 .. 1, t = 0 .. 2*Pi), animate(plot, [[[0, a], [cos(a), a]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[0, a], [cos(a), a]], color = green, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), implicitplot(y = sin(2*t), t = 0 .. 2*Pi, y = -1 .. 1), animate(plot, [[[a, 0], [a, sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[a, 0], [a, sin(2*a)]], color = red, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [a, sin(2*a)]], linestyle = dash, color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [cos(a), a]], linestyle = dash, color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100));
 

Hi! I was wondering about drawing phase plane for differential system with some conditions. For example how can we draw this for:

restart;
with(plots);
with(DEtools);

ode := piecewise(1 < abs(x(t)), diff(x(t), t $ 2) - 2 = 0, abs(x(t)) < 1, diff(x(t), t $ 2) = 0);
????????????

I wanted something similar to that:

DEplot({diff(x(t), t) = y(t), diff(y(t), t) = 8*x(t)*y(t)}, [x(t), y(t)], t = -2 .. 2, x = -1 .. 1, y = -4 .. 4);

or this:

ode1 := diff(x(t), t $ 2) + 2*diff(x(t), t) = 0

DEplot(ode1, x(t), t = -2 .. 10, [[x(1) = 0.2, D(x)(1) = -1.4]]);

Edit:

I rewrite that to make integral curves and this phase plot should look similar to this: