Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 3 - Second Order Linear Equations - 3.2 Solutions of Linear Homogenous Equations; the Wronskian - Problems - Page 155: 8



Work Step by Step

$$(t-1)y''-3ty'+4y=sint,\quad{y(-2)}=2,\quad{y'(-2)}=1$$ For a unique solution that is twice differentiable, the $y''$ term has to exist. Hence $t=1$ is a limit of the boundary. Since the given solution $t=-2$ lies to the left of this limit, there is a confirmed solution in the range $t<1$. Hence, the longest open interval is $t<1$.
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