# Prove Picard's Existence and Uniqueness Theorem on Different Levels

Desvl at
IVP and Picard’sBy IVP (Initial Value Problem), we mean the problem about solving\begin{cases}\frac{dy}{dx}=f(x,y) \\y(x_0)=y_0\end{cases}Of course we do hope we can solve this problem easily with a simple result. But that won’t happen if the function $f$ is ‘ugly’ enough. Hence the problem is, gene……