0006.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. 

\[ -{\left(t + 5\right)} {\left(t - 2\right)} - {y''} = {\left(t - 5\right)} {y'''} e^{t} + y e^{t} \hspace{2em}
      x( 2 )= 8 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-\infty,5)\]
\end{exerciseAnswer}