0005.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. 

\[ {\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em}
      x( 0 )= -5 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-2,+\infty)\]
\end{exerciseAnswer}