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

\[ -{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2 \]