<exercise masterit-seed="2568" masterit-slug="N1" masterit-name="Existence/uniqueness theorem for linear IVPs"><statement><p>
Find the largest interval for which the Existence and Uniqueness
Theorem for Linear IVPs guarantees a unique solution for the following IVP.
</p><me> -{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em}
x( -3 )= -8 </me></statement><answer><me>(-4,1)</me></answer></exercise>
