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. 

\[ {\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em}
      x( -2 )= 3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-5,2)\]
\end{exerciseAnswer}