Existence, Uniqueness & Bifurcations · Challenge problem

The state of a system obeys $y' = h + 3y - y^3$, where the parameter $h$ changes very slowly. It starts at the largest equilibrium when $h = 3$, and $h$ is then decreased slowly, the state tracking its equilibrium. At some value of $h$ that equilibrium disappears and the state jumps to a distant stable equilibrium. What value of $y$ does it jump to?