I'm was stubling on the question of uniqueness of differential equations. I have a differential equation of the form $ \frac{d}{dt}y(t)= f(t)y(t), y(t\_0)=p\_0$ ie. a linear, first order differential equation and it seems to be the case, that one of the ways to determine uniqueness of the solutionfunction is to require continuity on a open interval of f(t). I couldn't find example which were not unique, could only find some where the diff. eq. was nonlinear. My question, does such exist and can you give me an example?