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 11 - Boundary Value Problems and Sturm-Liouville Theory - 11.1 The Occurence of Two-Point Boundary Value Problems - Problems - Page 670: 6



Work Step by Step

General form of second order differential boundary value problem: $\mathcal{p}$($\mathcal{x}$)$\mathcal{y^{n}}$$\mathcal{+}$$\mathcal{q(x)y^{1}+r(x)y=g(x)}$ $\mathcal{y(x_{0})=y_{0}}$ $\mathcal{y(x_{1})=y_{1}}$ Equation is homogeneous if $\mathcal{g(x)}$ and $\mathcal{y_{0}=y_{1}=0}$ $\mathcal{-y^n+\leftthreetimes(1+x^2)y}$ $\mathcal{-y^n-\leftthreetimes(1+x^2)y=0}$ Since $\mathcal{g(0)}$=$\mathcal{0}$, $\mathcal{y_0=y_1=0}$ equation is homogeneous
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