linguistic:paraphrasing
Solutions of Finite Duration

For non-linear autonomous ODEs it is possible under some conditions to develop solutions of finite duration, meaning here that from its own dynamics, the system will reach the value zero at an ending time and stays there in zero forever after. These finite-duration solutions cannot be analytical functions on the whole real line, and because they are non-Lipschitz functions at their ending time, they are not unique solutions of Lipschitz differential equations.

As example, the equation:

Admits the finite duration solution: