My problem is:

Let x1(t) and x2(t) be two particular solutions of an ordinary differential equation with a separable right hand side. Is it possible that x1(t1) =x2(t1) for some t1?

My answer would be:
It is not possible, because the results for t1 are locally unique. The only exception could happen, if x1 and x2 are zero.

Is this correct?