Determine the largest interval (a, b) for which Theorem 1 guarantees the existence of a unique solution on (a, b) to the given initial value problem.

$$\begin{gathered} \mathbf{y}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{-}\sqrt{\mathbf{x}}\mathbf{y}\mathbf{=}\mathbf{sinx} \\ \mathbf{y}\left(\pi \right)\mathbf{=}\mathbf{0}\mathbf{,}\mathbf{ }\mathbf{ }\mathbf{y}\mathbf{\text{'}}\left(\pi \right)\mathbf{=}\mathbf{11}\mathbf{,}\mathbf{ }\mathbf{ }\mathbf{y}\mathbf{\text{'}}\mathbf{\text{'}}\left(\pi \right)\mathbf{=}\mathbf{3} \end{gathered}$$

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