0009.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. 

\[ -{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em}
      x( -5 )= -10 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-6,+\infty)\]
\end{exerciseAnswer}