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Unformatted text preview: MATH 2930 Introduction to Diﬀerential Equations Worksheet 10, October 30 2008 Sections 203, 208, 211
October 29, 2008 1 Problem 3.8 #13 – Boundary Value Problem
y ′′ + 2y ′ + λy = 0; y(0) = y(1) = 0. (1) Consider the eivenvalue problem a) Show that λ = 1 is not an eigenvalue. b) Show that there is no eigenvalue λ such that λ < 1. 2 Problem 3.5 #27 – Undetermined Coeﬀ.’s Set up the appropriate form of a particular trial solution yp , but do not determine the values of the coeﬃcients. y (4) + 5y ′′ + 4y = sin x + cos 2x (2) 3 Problem 8.1 #5 – Power Series Approach Find a power series solution of the given d.e., and determine the radius of convergence of the resulting series. Use the series in Eqs. (512) to identify the series solution in terms of familiar elementary functions. y ′ = x2 y 2. (3) 1 4 Problem 8.1 #17 – Power Series Approach Find two linearly independent power series solutions of the given d.e. Determine the radius of convergence of each series, and identify the general solution in terms of familiar elementary functions. x2 y ′ + y = 0. (4) 2 ...
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This note was uploaded on 11/09/2008 for the course MATH 2930 taught by Professor Terrell,r during the Fall '07 term at Cornell.
 Fall '07
 TERRELL,R
 Equations

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