function [] = prob_3_17
% 
% 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.
% 
%-----

Pe = 1; R = 2; n = 2;

guess = [ 0.5; 0 ];
solinit = bvpinit(linspace(0,1,10),guess);  
sol = bvp4c(@f,@bcs,solinit,[],Pe,R,n);
disp( 'Solution values of interest' ); 
deval( sol, [ 0, 1 ] )

figure; 
plot( sol.x, sol.y(1,:), '-bo' ); hold on; 
grid on;

function [res] = bcs(ya,yb,Pe,R,n)
% BCS - 
%      

res = [ ya(2)-Pe*(ya(1)-1);
        yb(2);
      ];


function [ ode ] = f(x,y,Pe,R,n)
% F - 
% y(1)=y(t); y(2)=y'(t); 
% 

ode = [  
    y(2);
    Pe*(y(2)+R*(y(1)^n));
      ];