## Question on dynamic of $y'(t)=\sin(y(t))$ and on nature of equilibrium point of $y’=|\sin(y)|$.

Let $$y’=\sin(y)$$ an ODE. I just try to imagine the dynamic behind.

Q1) First, on $$\mathbb R$$ we only have $$\mathcal C^1$$ piecwise solution, no ? Because, when for example $$y(t_0)\in (0,\pi/2)$$, then, $$y(t)\to \pi/2$$, and when the particle will arrive in $$\pi/2$$, then it will sotp and never go again. And so, I can’t get a smooth solution on $$\mathbb R$$. Am I right ?

Q2) Now, if $$y’=|\sin(y)|$$, what will be the nature of $$y=\pi$$ ? Because it’s an equilibrium point, but it will be stable at left and unstable at right. Can I call it a saddle ?