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

\[ {\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3 \]