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How would you do this in Maple? Does such a feature exist?

restart; with(DEtools); phaseportrait([(D(x))(t) = -.1+x(t)^2-x(t)*y(t), (D(y))(t) = y(t)^2-x(t)^2-1], [x(t), y(t)], t = -10 .. 10, [[x(0) = 0, y(0) = 1], [x(-2) = -2, y(-2) = -1], [x(0) = 1, y(0) = 0], [x(0) = 0, y(0) = 0]], stepsize = 0.5e-2, scene = [x(t), y(t)], linecolor = t, x = -4 .. 4, y = -3 .. 3) I want to explicitly draw the hyperbola with arrows in the direction of the vector field. How do I obtain this? With the initial conditions I get solution curves that I dont want.

restart; with(DEtools) x1 := diff(x(t), t) = (4-x-4*y)*x; y1 := diff(y(t), t) = (4-4*x-y)*y; phaseportrait([diff(x(t), t) = (4-x-4*y)*x, diff(y(t), t) = (4-4*x-y)*y], [x(t), y(t)], x = -20 .. 20, y = -20 .. 20, t = -2 .. 2, [[x(0) = 0, y(0) = 1]], stepsize = 0.5e-1, scene = [y(t), x(t)], linecolour = sin((1/2)*t*Pi), method = classical[foreuler]) I'm trying to specify the domain for x and y but I receive the following error Error, (in DEtools/phaseportrait) initial conditions must be specified in inits The above works when I get rid of x = -20 .. 20, y = -20 .. 20,

I'm to generate a random matrix ie > with(LinearAlgebra); > RandomMatrix(2, 2, generator = -1 .. 1); and find the eigenvalues of each matrix ten times. How do I put random Matrix in the for loop with Maple?

ODE:=theta'(t)=mu+sin(theta(t)); V(t):=cos(theta(t)); I need to Plot V(t) for various IC. An assumption I can make is mu