I am trying to find an example of ode, $x^{‘}=f(t,x)$, where $f$ does not satisfies Picard-Lindelöf theorem, but it still have unique solution.

Is it possible?


Yes, it is.

  1. Osgood's criterion
  2. $f(t,x)$ is decreasing as a function of $x$ for all $t$.

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