0000.ptx

<exercise masterit-seed="0368" masterit-slug="X2" 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 - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em}
      x( 1 )= 7 </me>
  </statement>
  <answer>
    <me>(-4,5)</me>
  </answer>
</exercise>