0002.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. 

\[ {\left(t + 5\right)} t {y'''} = -t^{2} - {\left(t - 5\right)} y - 4 \, {y''} - 16 \hspace{2em}
      x( -1 )= 1 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-5,0)\]
\end{exerciseAnswer}