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plotting - How to visualize slope fields of differential equations without vectors?


I'm looking to visualize slope fields of differential equations for my differential equations course. Every example I see draws them as vectors, adding unnecessary "arrows" that, to me, are visually distracting. Is there a way to plot these slope fields without the "arrows" that get in the way?



Answer



You can use the options VectorScale and VectorStyle of VectorPlot. To create the slope field for the first order equation $y'=f(x,y)$, I usually do something like so.


f = Exp[-x] - y;

VectorPlot[{1, f}, {x, -2, 2}, {y, -2, 2},
  VectorScale -> {0.03, Automatic, None},
  VectorStyle -> {Gray, Arrowheads[0]}]

enter image description here


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