2015-03-20 10:10:49 +0100 received badge ● Nice Answer (source) 2013-01-17 16:45:55 +0100 received badge ● Teacher (source) 2012-11-07 07:43:27 +0100 received badge ● Editor (source) 2012-11-07 07:41:25 +0100 answered a question Phase portraits of 2-dimensional systems The following function allows you to move the initial point and determines the "corners" of the picture with respect to the maximum an minimum values of the solutions. @interact def syst(x0=slider(-2,2,0.1,0.5),y0=slider(-2,2,0.1,0.5)): x,y=var('x y') vect=[-y,-x] sol=desolve_odeint(vect,[x0,y0],srange(-4,4,0.1),[x,y]) xmin=sol[0,0] xmax=sol[0,0] ymin=sol[0,1] ymax=sol[0,1] for i in range(0,len(sol)): if sol[i,0] > xmax: xmax=sol[i,0] if sol[i,0]< xmin: xmin=sol[i,0] for i in range(0,len(sol)): if sol[i,1] > ymax: ymax=sol[i,0] if sol[i,1]< ymin: ymin=sol[i,0] p1=plot_vector_field((vect[0],vect[1]),(x,xmin-2,xmax+2),(y,ymin-2,ymax+2),plot_points=60) p=line(zip(sol[:,0],sol[:,1])) (p+p1).show(aspect_ratio=1)  Of course the solution using maxima is the nicest.