How to Plot the Direction Field and Integral Curves Correctly with Plots

General Usage
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4

Ah okay, so it looks like you’re plotting the gradient field when you actually want the slope field. When you change it out the plots match:

using Plots
gr()
#gr(size=(600,400))

function example()
  X = range(-2, stop=2, length=50)
  Y = range(-2, stop=2, length=50)
  f(x, y) = -x^3 + 3y - y^3
  contour(X, Y, f)

  x = range(-2, stop=2, length=15)
  y = range(-2, stop=2, length=15)


  dydx_norm(x, y) = [1; x^2/(1 - y^2)] / 25

  quiver!(repeat(x,11), vec(repeat(y',11)), quiver=dydx_norm, c=:blue)

  xlims!(-2, 2)
  ylims!(-2, 2)
    
  # to save as png uncomment the code below and gr(size=(600,400))
  #png("example")
end

example()

slope_field
slope_field1920×1280 185 KB

The default plot options look kind of bad for this plot. I would actually recommend using Makie.jl for something that looks as good as the Maple/Mathematica version (also not need to manually normalize your plot):

using CairoMakie

fig = Figure()
ax = Axis(fig[1,1])

X = range(-2, stop=2, length=50)
Y = range(-2, stop=2, length=50)
f(x, y) = -x^3 + 3y - y^3

contour!(X, Y, f, color = :blue, linewidth=2)

dydx(x,y) = Point2f(1, x^2/(1 - y^2))

streamplot!(dydx, -2.0..2.0, -2.0..2.0, colormap=:blues)

fig

makie_plot
makie_plot800×600 136 KB

Hope that clears things up!

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