i've got the dynamical system:

xdot=-2x

ydot=-y

Now I have solved the system and found the general solution:

x(t)=Ae(^-2t)v +Be(^-t)u, wherev=(1,0),u=(0,1), A,B=constants

Now, it can be shown that dy/dx=y/2x, hence dy/dx=0 only when y=0, and for positive x and y dy/dx>0

however, as x=Ae(^-2t), and y=Be(^-t), we have that if t is negative, x is larger than y, and if t is positive, y is larger than x, implying dy/dx = 0 at some point x>0,y>0 (assuming for example the 2 constants are positive and equal).

How is this possible?