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The phase portrait gives you $y'$ as a function of $y$ in multiple pieces (all those intervals where the former is actually a unique function). In each such piece, you can in principle find the functional form $dy/dt = y' = g(y)$ by inspection. Next, how to get the time? Use $$t-t_i = \int \frac{dy}{g(y)}$$ which is then solvable for $y(t-t_i)$ in ...