Document page: 10 of pdf\page number 9
I am not undertanding this part:
Then the elementary existence theorem for solutions of first order ordinary differential equations implies that eq. 2.17 defines an n-parameter family of curves in the region $G$, such that each point in $G$ has a unique curve pass through it
Suppose I have a solution $x = \alpha t + \beta t^2$,(a 2-parameter family of curves) then the point $(x,y,t) = (0,0,0)$ does not have a unique curve as both this curve: $x = t + t^2$ and this curve: $x = 2t + 2t^2$ go through the point $(0,0,0)$
It is obvious that I am not understanding some thing here (this whole congruence of curves part is a bit confusing) and would really appreciate any help you can provide. Also if possible an example.