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 4 - Higher Order Linear Equations - 4.1 General Theory of nth Order Linear Equations - Problems - Page 225: 23



Work Step by Step

We will use Abel's formula to find wronskian ${y}'''+\frac{2}{t}{y}''-\frac{1}{t}{y}'+y=0\\\\$ $p_{1}(x)=\frac{2}{t}\;\;\;\;\;\;\;\;\;\;$ coefficient of ${y}''\\\\$ $W(t)= Ce^{-\int p_{1}(x)dx}\;=\;Ce^{-\int (\frac{2}{t})dx}\;=Ce^{-2\;ln|t|}\;=Ce^{ln\frac{1}{t^2}}\;=$ $\;c.\frac{1}{t^2}\;=\;\frac{c}{t^2}\\\\$ $W(t)=\;\frac{c}{t^2}$
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