Sorry, once more:

restart;

with(DEtools):with(plots):

vx := diff(x(t), t) = -(x(t)-y(t))/sqrt(x(t)^2+y(t)^2);

vy := diff(y(t), t) = -(x(t)+y(t))/sqrt(x(t)^2+y(t)^2);

sys := {vx, vy}:

init := [[x(0) = 1, y(0) = 1], [x(0) = 1, y(0) = -1], [x(0) = -1, y(0) = -1], [x(0) = -1, y(0) = 1]]:

animate(DEplot, [sys, [x(t), y(t)], t = 0 .. T, x = -1 .. 1, y = -1 .. 1, init, stepsize = 0.1e-1, thickness = 1, arrows = none, title = "Animace", linecolor = [red, blue, gold, black]], T = 0.1e-2 .. sqrt(2));

It's all right already. Thank you!!! :-)

Maple10...

Maple write this mistake:

Error, (in DEtools/DEplot/AnalyseOptions) Option keyword (animatefield) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid,

obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {scaling, symbol, axes,

title, thickness, resolution, axesfont, labelfont, xtickmarks, coords, color, colour, linestyle, style, view, font, titlefont}, or one of the allowed dsolve/numeric options:

{method, start, initial, stepsize, abserr, control, ctrl, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, minrel, minstep, relerr, value, stiff, corrections,

errorper, startinit, tolerance, maxfevals}

OK, thank you. I write this:

gr1 := DEplot(sys, [x(t), y(t)], t = 0 .. sqrt(2), x = -1 .. 1, y = -1 .. 1, [[x(0) = 1, y(0) = 1]], stepsize = 0.1e-1, thickness = 1, arrows = none, linecolor = red):

gr2 := DEplot(sys, [x(t), y(t)], t = 0 .. sqrt(2), x = -1 .. 1, y = -1 .. 1, [[x(0) = 1, y(0) = -1]], stepsize = 0.1e-1, thickness = 1, arrows = none, linecolor = blue):

gr3 := DEplot(sys, [x(t), y(t)], t = 0 .. sqrt(2), x = -1 .. 1, y = -1 .. 1, [[x(0) = -1, y(0) = -1]], stepsize = 0.1e-1, thickness = 1, arrows = none, linecolor = gold):

gr4 := DEplot(sys, [x(t), y(t)], t = 0 .. sqrt(2), x = -1 .. 1, y = -1 .. 1, [[x(0) = -1, y(0) = 1]], stepsize = 0.1e-1, thickness = 1, arrows = none, linecolor = black):

display([gr1, gr2, gr3, gr4]);

I need animation this curve. I want to depict gradually it. Is it instruction command "animate"?