> lorenz:=diff(x(t),t)=sigma*(y(t)-x(t)),
diff(y(t),t)=r*x(t)-y(t)-x(t)*z(t),
diff(z(t),t)=x(t)*y(t)-b*z(t);

> sigma:=10:

> b:=8/3:

> r:=28:

> ff:=dsolve({lorenz,x(0)=.2,y(0)=.1,z(0)=.5 },{x(t),y(t),z(t)},type=numeric,output=listprocedure);

> fx:=subs(ff,x(t));

> fy:=subs(ff,y(t)): fz:=subs(ff,z(t)):

> fx(0);

> fx(0.3);

> with(plots):
odeplot(ff,[t,x(t)],0..100);

Warning, the name changecoords has been redefined

Warning, cannot compute solution further right of 86.8255095722534236

> odeplot(ff,[t,y(t)],0..60);

> odeplot(ff,[t,x(t)],0..60);

> odeplot(ff,[t,z(t)],0..60);

> odeplot(ff,[x(t),y(t)],15..60);

> odeplot(ff,[x(t),y(t),z(t)],10..50);

> chaos:=dsolve({lorenz,x(0)=-3.,y(0)=-3.,z(0)=19. },{x(t),y(t),z(t)},type=numeric,output=listprocedure);

>

> odeplot(chaos,[t,x(t)],0..60);

> odeplot(chaos,[t,y(t)],0..60);

> odeplot(chaos,[t,z(t)],0..60);

> odeplot(chaos,[x(t),y(t)],0..60);

> odeplot(chaos,[x(t),y(t),z(t)],0..60);

>