Example from lecture on Wed., Feb 27.
Based on Problem #1 in Section 9.3.

> with(DEtools):

> dfieldplot([D(x)(t)=x(t)-y(t)^2,
D(y)(t)=x(t)-2*y(t)+x(t)^2],
[x(t),y(t)],t=0..1,x=-2..2,y=-2..2);

> phaseportrait([D(x)(t)=x(t)-y(t)^2,
D(y)(t)=x(t)-2*y(t)+x(t)^2],
[x(t),y(t)],t=-10..40,[[x(0)=.003,y(0)=.001],[x(0)=.5,y(0)=1.4],
[x(0)=.5,y(0)=1.5]],x=-2..2,y=-2..2,
linecolor=[blue,green,red],color=black,stepsize=.01);

What happens above if you leave out "stepsize"? Can you explain?

> dfieldplot([D(x)(t)=x(t)-y(t)^2,
D(y)(t)=x(t)-2*y(t)+x(t)^2],
[x(t),y(t)],t=0..1,x=-20..20,y=-20..20);

Just for fun see what dsolve does!

> dsolve({diff(x(t),t)=x(t)-y(t)^2,diff(y(t),t)=x(t)-2*y(t)+x(t)^2});

> dsolve({diff(x(t),t)=x(t)-y(t)^2,diff(y(t),t)=x(t)-2*y(t)+x(t)^2,x(0)=3,y(0)=1});

>