Thanks alot.

 

But how to sketch the arrow on these solution curves?

Thanks alot.

 

But how to sketch the arrow on these solution curves?

Set a[1] = 2 and a[2] = 4/3

restart; with(plots); with(DEtools); plot1 := phaseportrait([(D(x))(t) = x(t)+exp(-y(t)), (D(y))(t) = -y(t)], [x(t), y(t)], t = -100 .. 100, [[x(0) = 0, y(0) = 1]], x = -2 .. 2, y = -2 .. 2, titlefont = [TIMES, ROMAN, 18], title = `6.1.14`, color = grey, linecolor = [red, blue]); plot2 := plot(a[1]*(x(t)+1)+a[2]*(x(t)+1)^2, x = -2 .. 2, color = green); display([plot1, plot2]) The above problem only had DE, I have 2. What do I need to change in plot2 to make this work>

Nevermind I got it

Nevermind I got it

After that, then I apply the conditions as follows:

 

restart; with(LinearAlgebra); Totals := [0, 0, 0, 0, 0]; to 100 do A := RandomMatrix(2, 2, generator = -1 .. 1); if `and`(Determinant(A) < 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[1] := Totals[1]+1 elif `and`(Trace(A) > 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[2] := Totals[2]+1 elif `and`(Trace(A) > 0, Trace(A)^2-4*Determinant(A) < 0) then Totals[3] := Totals[3]+1 elif `and`(Trace(A) < 0, Trace(A)^2-4*Determinant(A) < 0) then Totals[4] := Totals[4]+1 elif `and`(Trace(A) < 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[5] := Totals[5]+1 else print("Nothing") end if end do; Totals/(100.0)

After that, then I apply the conditions as follows:

 

restart; with(LinearAlgebra); Totals := [0, 0, 0, 0, 0]; to 100 do A := RandomMatrix(2, 2, generator = -1 .. 1); if `and`(Determinant(A) < 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[1] := Totals[1]+1 elif `and`(Trace(A) > 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[2] := Totals[2]+1 elif `and`(Trace(A) > 0, Trace(A)^2-4*Determinant(A) < 0) then Totals[3] := Totals[3]+1 elif `and`(Trace(A) < 0, Trace(A)^2-4*Determinant(A) < 0) then Totals[4] := Totals[4]+1 elif `and`(Trace(A) < 0, Trace(A)^2-4*Determinant(A) > 0) then Totals[5] := Totals[5]+1 else print("Nothing") end if end do; Totals/(100.0)

I need to generate a matrix

a b

c d

 

where a b c d are from [-1,1]

I need to generate a matrix

a b

c d

 

where a b c d are from [-1,1]

Rather than have Maple print text, what's the Maple command to store these elements ('types') for each matrix? Then divide by 10 to find the relative frequency?

Rather than have Maple print text, what's the Maple command to store these elements ('types') for each matrix? Then divide by 10 to find the relative frequency?

I got it working anyway thanks tho

I got it working anyway thanks tho

Nevermind, but if I want to label the funciton in the graph, how do I do this?