Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP.
\[ {\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2 \]
Answer:
\[(2,+\infty)\]