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. 

\[ e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em}
      x( 3 )= -9 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-6,5)\]
\end{exerciseAnswer}