0000.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. 

\[ -{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em}
      x( 1 )= 7 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-4,5)\]
\end{exerciseAnswer}