# graphics – Problems encountered when drawing direction fields

I've learned to draw directional fields according to @Robert Jacobson's answer to the question How can I plot the direction field of a differential equation? However, when I tried to draw the direction field for $$dfrac {dy} {dx} = dfrac {x} {y}$$, the direction field produced was false.

That's what I got:

Gradients at y = 0 are assumed to be at infinity and there must be vertical red line segments on the x-axis. I can not understand why.

``````F[x_, y_] : = x / y

VectorPlot[{1, F[x, y]} / Sqrt[1 + F[x, y]^ 2], {x, -3, 3}, {y, -3, 3},
VectorScale -> 0.025, VectorPoints -> 13, VectorStyle -> {"Segment", Red}, Frame -> None,
Axes -> True, AxesStyle -> Directive[Black, 15.5, FontFamily -> "Times", Arrowheads[.03]],
AxesLabel -> {x, y}, Ticks -> {{-3, {-2.5, ""}, -2, {-1.5, ""}, -1, {-0.5, ""}, 0, { 0.5, ""}, 1, {1.5, ""}, 2, {2.5, ""}, 3}, {-3, {-2.5, ""}, -2, {-1.5, ""}, -1, {-0.5, ""}, 0, {0.5, ""}, 1, {1.5, ""}, 2, {2.5, ""}, 3}}]
``````