DE24 Introduction to First-order Systems of ODEs

when the prof. says "I cannot predict just from this picture", at that time, the picture only depicts the solution x = x(t), y = y(t), it is only a parametrized curve without the red arrows. But if you substitute the solution x, y into the system, then we can get x'(t), y'(t) which describe the velocity in x,y directions.  the magnitude of x'(t), y'(t) do give the length of the velocity in x,y directions, so the total length will be (x'(t)^2 + y'(t)^2)^(1/2), i.e. the total magnitude of velocity.