In this video, I prove the famous Picard-Lindelöf theorem, which states that, if f is Lipschitz, then the ODE y’ = f(y) with a given initial condition always has a unique solution (at least in the local sense). The proof involves some neat analysis; more precisely we use the Banach fixed point theorem, featured in another video of mine. Finally, I’ll give some examples of non uniqueness and nonexistence when the assumptions aren’t satisfied. Enjoy!
