Hi all,
I have the following D.E.
$\displaystyle \frac{dy}{dt} = \sqrt{y^2+1},\\ y(t_0) = y_0$
How can i find a value of $\displaystyle y_0$ and a value of $\displaystyle t_0$ such that there is a unique solution to the initial-value problem?
Hi all,
I have the following D.E.
$\displaystyle \frac{dy}{dt} = \sqrt{y^2+1},\\ y(t_0) = y_0$
How can i find a value of $\displaystyle y_0$ and a value of $\displaystyle t_0$ such that there is a unique solution to the initial-value problem?
The functions
$\displaystyle f(t,y)=\sqrt{y^2+1},\;\;\dfrac{\partial f}{\partial y}$
are continuous on $\displaystyle \mathbb{R}^2$ , so for every $\displaystyle (t_0,y_0)\in \mathbb{R}^2$ there exists a unique solution satisfying $\displaystyle y(t_0)=y_0$ .