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 224: 4

Answer

The solutions of the given equation are sure to exist on $(0,+\infty)$

Work Step by Step

The given higher order linear equation is written in the form : $\frac{d^ny}{dt^n}\;+\;p_{1}(t)\frac{d^{n-1}y}{dt^{n-1}}\;+\;.........\;+\;p_{n-1}\frac{dy}{dt}\;+\;p_{n}(t)y\;=\;g(t)\\\\ $ $n=3\;\;\;\;\;\;\;\;\;\;p_{1}(t)=t\;\;\;\;\;\;\;\;\;\;p_{2}=\frac{e^t}{t(t-1)}t^2\;\;\;\;\;\;\;\;p_{3}(t)=t^3\;\;\;\;\;\;\;\;\;\;g(t)=ln(t)\\\\$ $p_{1},p_{2},p_{3}$ are continuous everywhere on $\mathbb{R}.$ $g$ is continuous everywhere on its domain $(0,+\infty)$ The solutions of the given equation are sure to exist on $(0,+\infty)$
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