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answered 6 years ago

calc314 gravatar image

Here is another option for plotting. The streamline_plot does a nice job of plotting some sample curves along with arrows to give direction. I like to use the odeint solver since it works for systems so nicely. Here I use it by defining a system ds/dt=1,dx/dt=x24x. This gives the appropriate plot. Note that we have to tell Sage that the number 1 should be in the symbolic ring (SR) to get this to work.

var('x s t')
pp=streamline_plot(x^2-4*x,(t,0,5),(x,-4,5))
initialvalues=[-2,2]
for x0 in initialvalues:
    pp+=line(desolve_odeint([SR(1),x^2-4*x],[0,x0],srange(0,5,0.05),[s,x]),color='red',thickness=3)
pp.show(ymin=-4,ymax=5)