Models & Qualitative Behavior · Superchallenge problem

A ball is thrown straight up at $10$ m/s and moves with quadratic air resistance: while rising $v' = -10 - \dfrac{v^2}{10}$, and while falling (taking downward as positive) $v' = 10 - \dfrac{v^2}{10}$ ($v$ in m/s, $t$ in s). With what speed (in m/s) does it return to the thrower's hand? Give an exact answer.