> [!Example] Example (non-uniqueness) > Consider the [[Initial Value Problem for Scalar Ordinary Differential Equation|IVP]] $\frac{d}{dt}x(t)=\sqrt{ x(t) }$subject to $x(0)=0.$ > > The function $x(t)=0$ for all $t$ is a solution. Moreover, for any $c>0$ the function $x_{c}(t)= \begin{cases} 0 & \text{if } t\leq c, \\ \frac{(t-c)^{2}}{4} & \text{otherwise} \end{cases}$is a solution. Indeed if $t>c$ then $x_{c}'(t)= \frac{d}{dt} \left( \frac{(t-c)^{2}}{4} \right) = \frac{t-c}{2} = \sqrt{ \frac{(t-c)^{2}}{4} }=\sqrt{ x_{c}(t) }$and if $t<c$ then $x_{c}'(t)=0=\sqrt{ x_{c}(t) }$