Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be analytic and consider the ODE $$x'(t)=f(x(t)).$$ It is well-known that if $(t_{min},t_{max})$ is the maximal domain of a solution $x$ and $t_{max}<\infty$, then $$\lim_{t\to t_{max}}|x(t)|=\infty.$$ Let $t_0\in(t_{min},t_{max})$. What conditions on $f$ (appart from linearity) ensure that $$\int_{t_0}^{t_{max}}|x(t)|^2dt=\infty,\quad\text{when }t_{max}<\infty?$$