# Cauchy Problem - Why no unique solution? [closed]

Why does the Cauchy problem $$\begin{cases} y'= y^{3/4},\\ y(0)=0 \end{cases}$$

not admit a unique solution? And please how we justify that $(y^{3/4})'$ is not continuous?

## closed as off-topic by Dylan, Leucippus, JonMark Perry, Ethan Bolker, Brian BorchersMay 24 '18 at 2:18

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• Probably because $y(x)=0$ is a trivial solution. – Alexis Olson May 23 '18 at 18:58
• have a look at my thorough study here math.stackexchange.com/questions/2173984/… – zwim May 23 '18 at 19:46
• a unique solution exists on an interval if both $y^{3/4}$ and $(y^{3/4})'$ are continuous on the interval. The problem is that neither are continuous at $0$ – Vasya May 23 '18 at 19:59
• please how we justify that $(y^{3/4})'$ is not continuous? – rosy May 23 '18 at 20:21

Because $y(x) \equiv 0$ and $y(x) = \frac{x^4}{4^4}$ are solutions.
• please how we justify that $(y^{3/4})'$ is not continuous? – rosy May 23 '18 at 20:22
• Vadya tells in an comment that $(y^{3/4})'$ is not continuous. Furetheremore, if there is no unicity, then $(y^{3/4})'$ is not continuous. No? – rosy May 23 '18 at 21:41