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