I understand that the solution to the following is not unique:
$$y'=2ty^{1/3}.$$
However, why does this fact imply that "the solution you obtain via separation of variables must be 'glued' together with the equilibrium solution through piecewise definition"?
For context, I was asked this on an exam recently (the circled and correct equation is above):
One of the following four equations will require you to "glue" together solutions that you obtain via separation of variables with equilibrium solutions through piecewise definitions. First, circle the equation that requires this approach. Second, justify your answer.
Circle one: