Question

Please provide me the minimum y vector that will be computed in this domain.

Answer 1

clc;
clear all;
close all;
%% we wrote same code as given, just made some changes according to given equation
xleft=-1;
xright=1;
N=20;
x=linspace(xleft,xright,N);
x=x';
dx=(xright-xleft)/(N-1);
yleft=1;
yright=0.74; %%%if you solve given integral the max value of y you will get is 0.74
M=(diag(-2+ones(N,1),0)+diag(ones(N-1,1),-1)+diag(ones(N-1,1),1))/dx^2;
M(1,:)=[1, zeros(1,N-1)];
M(end,:)=[zeros(1,N-1),1];

b=x./(x+exp(-1.*x));
b(1)=yleft;
b(end)=yright;
%solve
y=M\b;
%plotting x vs y
plot(x,y);
xlabel('x');
ylabel('y');
title('given equation plot');
%%it will return minimun value of y vector on command window
min(y)