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: 9



Work Step by Step

$t(t-4)y''+3ty'+ty=2$ To use Theorem 3.2.1, divide both sides by $t(t-4)$: $y''+\frac{3}{t-4}y'+\frac{4}{t(t-4)}y=\frac{2}{t(t-4)}$ $p(t)=\frac{3}{t-4}$ which is continuous on $(-\infty,4) \cup(4,\infty) $ $q(t)=\frac{4}{t(t-4)}$ which is continuous on $(-\infty,0) \cup(0,4)\cup (4,\infty) $ $g(t)=\frac{2}{t(t-4)}$ which is continuous on $(-\infty,0) \cup(0,4)\cup (4,\infty)$ Thus, $p(t),q(t),$ and $g(t)$ are all continuous on $(-\infty,0) \cup(0,4)\cup (4,\infty)$ Since $t_0=3$, the solution exists on $(0,4)$
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