function [] = prob_3_23(T)
% 
% 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.
% 
%-----

beta = 0.5;
solinit = bvpinit(linspace(0,T,10), @guess);
sol = bvp4c(@f,@bcs,solinit,[],beta);

% Plot t v.s. y1(t):figure;
plot( sol.x, sol.y(1,:), '-bo' ); grid on;
fprintf( 'The value of D^2 f(0) = %f\n', sol.y(3,1) );

function [v] = guess(x)
  
  v = [ x;
	1;
	0 ];
   
function [res] = bcs(ya,yb,beta)
% BCS - 
%     
  res = [ ya(1);
	  ya(2);
	  yb(2);
      ];
      
function [ ode ] = f(x,y,beta)
% F - 
% y(1)=y(x); y(2)=y'(x); y(3)=y''(x);
% 
ode = [
    y(2);
    y(3);
    -y(1)*y(3) - beta*(1-(y(2)^2));
      ];