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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!!!

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

1 Answer 1

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 $t \geq 0$.

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

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