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

\[ 0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2 \]