= Solution
For an expanding universe with $0\leq w\leq1$, the coefficient $(1+3w)\mathcal H$ is positive. Thus $\Omega=1$ is unstable toward the future: an initial $0<\Omega<1$ decreases away from one toward zero, whereas an initial $\Omega>1$ increases and eventually corresponds to recollapse. In radiation domination, $w=1/3$ and
$$
\Omega'=2\mathcal H\Omega(\Omega-1),
$$
so a phase-line sketch has arrows away from the fixed point $1$ on both sides. Consequently the observed near-flatness today requires extremely fine tuning of the early value of $\Omega$.
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