# Some simple Maple commands for Phase Portraits
> with(DEtools):
# First we define the set of ODEs
> A:=[D(x)(t)=-y,D(y)(t)=x];
# Dfieldplot makes a aplot of the vector field.
> dfieldplot(A,[x,y],t=0..1,x=-1..1,y=-1..1,title="Harmonic
> Oscillator");
# An alternative derivative notation:s
> eqs:=[diff(x(t),t)=mu-(x(t))^2,diff(y(t),t)=-y(t)];
> dfieldplot(subs(mu=2.0,eqs),[x(t),y(t)],t=-2..2,x=-4..4,y=-4..4,arrows
> =SLIM);
# Here is another set of ODEs, the "Parrot"
> 	A := [D(x)(t)=y+y^2,D(y)(t)=-x+y/5-x*y+6*y^2/5];
> 	

# phaseportrait can draw trajecties as well
> phaseportrait(A,[x,y],t=-2..7,[[0,1.2,1.2],[0,1,.7],[0,0.1,0]],stepsiz
> e=0.02,title="Phase Portrait");
# Standard Example of Attracting fixed point that is not Lyapunov Stable
> r:= sqrt(x^2+y^2);
> f:= D(x)(t)=(x^2*(y-x)+y^6)/(r^2*(1+r^4));
> g:= D(y)(t)=(y^2*(y-2*x))/(r^2*(1+r^4));
> A:= [f,g];
> phaseportrait(A,[x,y],t=-0..10,[[x(0)=0.01,y(0)=0.1],[x(0)=-0.2,y(0)=0
> .1],[x(0)=-.1,y(0)=0.1],[x(0)=-0.05,y(0)=0.1]],stepsize=0.2);
> dfieldplot(A,[x,y],t=-10..10,x=-0.5..1,y=-0.5..1,title="Vector
> Field");