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

\[ {\left(t + 6\right)} {\left(t - 1\right)} {y''} + {\left(t - 6\right)} y + 4 \, {y'} = -t^{2} - 25 \hspace{2em} x( 0 )= -8 \]