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

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