# Math Help - Uniqueness Theorem

1. ## Uniqueness Theorem

Hi all,

I have the following D.E.

$\frac{dy}{dt} = \sqrt{y^2+1},\\ y(t_0) = y_0$

How can i find a value of $y_0$ and a value of $t_0$ such that there is a unique solution to the initial-value problem?

2. The functions

$f(t,y)=\sqrt{y^2+1},\;\;\dfrac{\partial f}{\partial y}$

are continuous on $\mathbb{R}^2$ , so for every $(t_0,y_0)\in \mathbb{R}^2$ there exists a unique solution satisfying $y(t_0)=y_0$ .