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Let us consider the following differential equation $$ \dot{x}(t)=a - b\sin(x(t)), \quad a,b\in\mathbb{R}. $$ My question. Suppose $a>|b|$ and $x(0)=x_0\in\mathbb{R}$. Can the solution to the ...

Consider the following ODE: $$ x′(t)=b(x(t)),\quad x(0)=x_0. $$ If $b$ is bounded and Holder continuous, then the Cauchy-Peano theorem ensures that there exists a solution to the above equation (but ...

Given two dynamical systems where $f$ is lipschitz for $x$ : $\begin{cases} x'(t)=af(x,t),\\ x(0)=x_0,\end{cases} t\in[0,\tau]$ and $\begin{cases} z'(t)=f(z,t),\\ z(0)=x_0,\end{cases} t\in[0,\tau']$, ...