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

\[ -{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8 \]