function [] = prob_3_24(X)
% 
% 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.
% 
%-----

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

% Plot t v.s. y1(t):figure;
figure; plot( sol.x, sol.y(1,:), '-bo' ); grid on;
title( [ 'X = ', num2str(X) ] );
fprintf( 'The value of DF(0) = %f\n', sol.y(2,1) ); 

function [v] = guess(x)
  
v = [ 1;
      1;
      1 ];

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