I am a newcomer to ODE. The relevant theorem that I can think of is about the maximum open interval of existence of the solution. But I have not learned to find the interval on which the solution exists.
$f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is $C^{1}$ and bounded on $\mathbb{R}^{n}.$ Is it possible to have a solution of $\dot{x}=f(x)$ that blows up in finite time?