Differential equation defined only on $(-1,1)$ We are going over differential equations, and I'm trying to think up of an example of a differential equation where the solution satisfying $x(0) = 0$ is defined for $t\in(-1,1)$, but I'm a bit stuck. Any help appreciated!

An example differential equation satisfying the given conditions would be $$(1-t^2)x'(t)^2=1$$ whose solutions with $x(0)=0$ are $x(t)=\pm\sin^{-1}t$. The inverse sine, of course, is only defined on $(-1,1)$.