I am just beginning to learn ordinary differential equation. My question:
Let : $t \in \mathbb{R}$, $x_0 \in \mathbb{R}$,
Let $f:\mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}: (t,x) \mapsto f(t,x)$.
Let $x:I \rightarrow \mathbb{R}:t \mapsto x(t)$, where $I \subseteq \mathbb{R}$ is the maximal interval of existence such that the solution of the following ordinary differential equation initial value problem:
$\frac{d}{dt}x = f(t,x), x(0)=x_0$
exists and is unique on $I$ (well-posed in the sense of Hadamard).
Is it possible that the solution $x$ has infinitely jump discontinuities?
Any comments, feedbacks, or inputs are very welcome. Thanks in advance.
Note: I have removed $d$ as to make things clearer.