restart;with(plots):with(plottools):with(DEtools):with(linalg):e1:=diff(x(t),t)=x(t)+y(t)-z(t);e2:=diff(y(t),t)=-x(t)+y(t)+z(t);e3:=diff(z(t),t)=x(t)-y(t)+z(t);dsolve({e1,e2,e3},{x(t),y(t),z(t)});dsolve({e1,e2,e3,x(0)=1,y(0)=-1,z(0)=0},{x(t),y(t),z(t)});E1:=diff(x(t),t)=x(t)*(1-y(t));E2:=diff(y(t),t)=.3*y(t)*(x(t)-1);#dsolve({E1,E2,x(0)=0,y(0)=1},{x(t),y(t)});DEplot([diff(x(t),t)=x(t)*(1-y(t)),diff(y(t),t)=.3*y(t)*(x(t)-1)],[x(t),y(t)], t=-7..7,[[x(0)=1.2,y(0)=1.2],[x(0)=1,y(0)=.7]],stepsize=.2);A:=matrix(3,3,[1,-3,3,3,-5,3,6,-6,4]);eigenvalues(A);eigenvectors(A);