Prove that if a trajectory starts at a noncritical point of the system dx dt = F( x, y)

QUESTION:

Prove that if a trajectory starts at a noncritical point of the system dx dt = F( x, y), dy dt = G( x, y), then it cannot reach a critical point ( x0, y0) in a finite length of time. Hint: Assume the contrary; that is, assume that the solution x = (t), y = (t) satisfies (a) = x0, (a) = y0. Then use the fact that x = x0, y = y0 is a solution of the given system satisfying the initial condition x = x0, y = y0 at t = a. 2