Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP.
\[ -{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10 \]
Answer:
\[(-6,+\infty)\]