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

\[ -{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8 \]