function sol = prob_3_15(abstol,reltol)
% 
% With input arguments I can play with the values of 
% the absolution and relative tolerances
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-18
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

bvpopts = bvpset( 'RelTol', reltol, 'AbsTol', abstol ); 
  
solinit = bvpinit(linspace(0,1,5),@guess);
sol = bvp4c(@odes,@bcs,solinit,bvpopts);
%plot(sol.x,sol.y(1,:));
%print -depsc ch3fig1a
%figure
xint = linspace(0,1,100);
Sxint = deval(sol,xint);
%plot(xint,Sxint(1,:));
%print -depsc ch3fig1b

figure; 
res = Sxint(2,:).^2 + 2*1*(exp(Sxint(1,:))-1)-Sxint(2,1)^2;
plot( xint, res, '-or' ); grid on; 

%=================================================
function v = guess(x)
v = [ x*(1-x); 1-2*x ];

function dydx = odes(x,y)
dydx = [ y(2); -exp(y(1)) ];

function res = bcs(ya,yb)
res = [ ya(1); yb(1) ];