VectorDensity = 9 (slider from 1 to 30, step 1)
VectorScale = 0.31 (slider from 0.01 to 1, step 0.01)
xStart: x(Corner[1])
yStart: y(Corner[1])
xStep: (x(Corner[3]) - x(Corner[1])) / VectorDensity
yStep: (y(Corner[3]) - y(Corner[1])) / VectorDensity
GridPts1 = Sequence(Sequence[(xStart + i * xStep, yStart + j * yStep), i, 0, VectorDensity], j, 0, VectorDensity)
GridPoints = Join(GridPts1)
NumPoints = Length(GridPoints)
f(x, y) = x / 2
A = (0.68, 2.84)
VecA = Vector(A, A + VectorScale * (1, f(x(A), y(A))))
GridVecs = Sequence(Vector[Vector[Element[GridPoints, k], Element[GridPoints, k] + VectorScale * (1, f(x(Element[GridPoints, k]), y(Element[GridPoints, k])))]], k, 1, NumPoints)
text1: "A=" + (LaTeX[A]) + ""
text2: "f(x,y)=" + (LaTeX[f]) + ""
B = (3.7800000000000002, 1.8800000000000001)
PathB = SolveODE(f, x(B), y(B), x(Corner[3]), (x(Corner[3]) - x(Corner[1])) / 200)
tMax = 20 (slider from 0.01 to 20, step 0.01)
Dx(x, y) = -y - 0.01 * x
Dy(x, y) = x
text3: "Dx(x,y)=" + (LaTeX[Dx]) + ""
text4: "Dy(x,y)=" + (LaTeX[Dy]) + ""
VecA2 = Vector(A, A + VectorScale * (Dx(x(A), y(A)), Dy(x(A), y(A))))
GridVecs2 = Sequence(Vector[Vector[Element[GridPoints, k], Element[GridPoints, k] + VectorScale * (Dx(x(Element[GridPoints, k]), y(Element[GridPoints, k])), Dy(x(Element[GridPoints, k]), y(Element[GridPoints, k])))]], k, 1, NumPoints)
PathB2 = SolveODE(Dy, Dx, x(B), y(B), tMax, tMax / 500)