# Consider the boundary-value problem y'' + y = 0, y(-) = y(), y'(-) = y'(). (a) The type of boundary

## Question:

Consider the boundary-value problem

y'' + y = 0, y(-π) = y(π), y'(-π) = y'(π).

(a) The type of boundary conditions specified are called periodic boundary conditions. Give a geometric interpretation of these conditions.

(b) Find the eigenvalues and eigenfunctions of the problem.

(c) Use a graphing utility to graph some of the eigenfunctions. Verify your geometric interpretation of the boundary conditions given in part (a).

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## Step by Step Answer:

**Related Book For**

## A First Course in Differential Equations with Modeling Applications

**ISBN:** 978-1111827052

10th edition

**Authors:** Dennis G. Zill

**Question Details**

Chapter #

**5**- Higher-Order Differential EquationsSection: Exercises 5.2

Problem: 33

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