0003.tex

\begin{exerciseStatement}


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

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