An ODE is a relationship such as $F(t,y(t),\dots,y^{(n)}(t))=0$ with $F:\Omega \subset R \times R^n \to R^n$, $\Omega$ open set not empty. What happens if $F$ is similar, but contains derivative of $y$ arbitrary large? Does anyone know where I can find some material that talks about this theme?
For example, the easiest thing that bumps in my mind: $\sum_{i=0}^{\infty} y^{(i)}=0$ Now, lets put initial conditions : $y^{(n)}(0)=n^2$ for all $n\in N$
What can I say about the solutions of this equation? I don't expect to calculate them analitically, but can I get some info? (Existence, unicity, global existence...)