function [] = prob_3_9(d,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.
% 
%-----

P = [ 1, 1 ];   
solinit = bvpinit(linspace(d,X),@guess,P);  
sol = bvp4c(@f,@bcs,solinit,[],d,X);
figure; 
p1 = plot( [ 0 sol.x], [ 1 sol.y(1,:)], '-bo' ); hold on; 
legend( [ p1 ], 'f(x)' ); 
grid on; title( [ '(d,X) = (', num2str(d),',',num2str(X),')' ] );
axis( [ 0 15 0 1 ] );
sol.parameters(1)

function [ v ]  = guess(x,P,d,X)
% GUESS - 
%

if( x < 1 )   
  v = [ 1; 0; ];
else
  v = [ 144*x^(-3); -432*x^(-4) ];
end


function [res] = bcs(ya,yb,P,d,X)
% BCS - 
%      
gamma = (1-sqrt(73))/2;  
  
res = [ ya(1) - ( 1 + P(1)*d + (4/3)*(d^(3/2)) + (2*P(1)/5)*(d^(5/2)) );
	ya(2) - ( P(1) + 2*sqrt(d) + P(1)*(d^(3/2)) );
	yb(1) - ( 144*X^(-3) + P(2)*X^gamma );
	yb(2) - ( -3*144*X^(-4) + P(2)*gamma*X^(gamma-1) ); 
      ];


function [ ode ] = f(x,y,P,d,X)
% F - 
% y(1)=y(x); y(2)=y'(x);
% 

ode = [  
    y(2); 
    (max(y(1),0)^(3/2))/sqrt(x);
      ];