# Initial value problem-unique solution

Could anyone help me to solve this exercise?

$${y}'=\sqrt{\left | y \right |}$$ $${y(0)=1/4}$$ $${t}\epsilon{[0,2]}.$$ Show that the initial value problem has a unique solution.

Thanks in advance!!!

-
$\LaTeX$ tip: use "\in" –  Stefan Smith Apr 7 '13 at 19:26

## 1 Answer

The function $g(y) = \sqrt{|y|}$ is Lipschitz on $[1/10, \infty)$, so your ODE has a unique solution for small $t > 0$. Since $y(t)$ is increasing, the ODE has a unique solution for $t \geq 0$.

-
Thank you...!!! –  mari Apr 11 '13 at 21:42