DO NOT ANSWER THIS QUESTION WITHOUT MATLAB!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

USE MATLAB TO PLOT THIS PROBLEM

HERE IS MY MATLAB CODE. USE IT AND FIX IT TO MATCH THE ANSWER GRAPH

clc

clear all

x = -2:1:2;

for n = 1:40

Cn = (2*pi)*(cos(n*pi) + 1);

F = Cn*sin(n*pi*x/2);

end

figure(1)

plot(x,F);

xlabel('x')

ylabel('y')

set(gca,'XAxisLocation','origin','YAxisLocation','origin')

THE SUPPOSED ANSWER

In each of Problems 1-6, find the expansion of f(x) in the eigenfunctions of the given Sturm-Liouville problem. Compare graphs of the function and the N th partial sums of the series for the given N. Also use the convergence theorem to determine what this eigenfunction expansion converges to on the relevant open interval. 1. y+y=0;y(0)=y(2)=0 f(x)=1xfor0x2,N=40 cn=1n2cos(n)+n2=n2(1+(1)n) Thus, the Eigen function expansion is given by n=1n2(1+(1)n)sin(2nx)