function [] = prob_3_7(Z)
% PROB_3_4 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-13
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

%Z = 2;
%Z = 3; 
%Z = 4; 

solinit = bvpinit(linspace(0,Z,30),@guess);  
sol = bvp4c(@f,@bcs,solinit);
figure; 
p1 = plot( sol.x, sol.y(1,:), '-bo' ); hold on; 
p2 = plot( sol.x, sol.y(3,:), '-go' ); 
legend( [ p1, p2 ], 'f(z)', 'h(z)' ); 
grid on; title( [ 'Z = ', num2str(Z) ] );
deval(sol,0.1)

function [ v ]  = guess(x)
% GUESS - 
%
v = [ 0; 0; 0; 0 ];
% $$$ v = [ exp(-sqrt(10)*x); -sqrt(10)*exp(-sqrt(10)*x);
% $$$       exp(-10*x); -10*exp(-10*x); ];
%v = [ -4; 0; +6; 0 ];

function [res] = bcs(ya,yb)
% BCS - 
%      
  
res = [ ya(1)-1;
	ya(3)-1;
	yb(1);
	yb(3); 
      ];


function [ ode ] = f(x,y)
% F - 
% y(1)=f(z); y(2)=f'(z); y(3)=h(z); y(4)=h'(z)
% 
  
beta = 10;   
lambda = 10;
E = 1; 

ode = [  
    y(2); 
    beta*(E-(y(3)/lambda))*y(1);
    y(4);
    lambda*beta*(E-(y(3)/lambda))*y(3);
      ];