Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP.

\[ t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10 \]