0007.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. 

\[ y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em}
      x( -3 )= 3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-5,1)\]
\end{exerciseAnswer}