Consider the initial value problem \left\{\begin{array}{l} y^{\prime}=\sqrt{x y} \\ y\left(x_{0}\right)=y_{0} \end{array}\right. Determine if we can guarantee the existence and uniqueness of the solution if \text { a. } x_{0}=3, y_{0}=0

\text {; } \text { b. } x_{0}=0, y_{0}=2 \text {; } \text { c. } x_{0}=1, y_{0}=-1 \text {. }