Maple Text Commands for Chapter 2 - PLANAR SYSTEMS 

>	restart:with(DEtools):with(plots):

 

Warning, the name changecoords has been redefined 

Example 4: Plot a phase portrait for the linear system  

>	iniset:={seq(seq([0,i,j],i=-2..2),j=-2..2)}: sys:=diff(x(t),t)=2*x(t)+y(t),diff(y(t),t)=x(t)+2*y(t):

 

Figure 2.8(a): Phase portrait with vector field superimposed. 

>	DEplot([sys],[x(t),y(t)],t=-5..5,iniset,stepsize=0.1,x=-3..3,y=-3..3,arrows=SLIM,color=black,linecolor=blue,thickness=2,font=[TIMES,ROMAN,15]);

 

Example 8: Plot a phase portrait for the nonlinear system  

>	iniset:={seq(seq([0,i,j],i=-2..2),j=-2..2)}: sys:=diff(x(t),t)=y(t),diff(y(t),t)=x(t)*(1-(x(t))^2)+y(t):

 

Figure 2.8(a): Phase portrait with vector field superimposed. 

>	DEplot([sys],[x(t),y(t)],t=-10..10,iniset,stepsize=0.1,x=-3..3,y=-3..3,arrows=SLIM,color=black,linecolor=blue,thickness=2,font=[TIMES,ROMAN,15]);

 

Exercise 4(d): Locating critical points. 

>	solve({2-x-y^2,-y*(x^2+y^2-3*x+1)},{x,y});

 

End of Chapter 2 Commands