function [] = prob_2_38()
% PROB_2_38 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-12
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

p = 4/3; 
a = exp( (1/3)*log(81/16) ); 
b = (27/40)*(1/a)^2;
x0 = .001; 

y0 = [ a*x0^p + b*x0^(p+1);
       a*p*x0^(p-1) + b*(p+1)*x0^p ];

[x,y] = ode45(@f,[x0 3],y0);
figure; plot( x, y(:,1), '-o' ); hold on; grid on; 
plot( x, a*x.^p + b*x.^(p+1), '-r' ); 

function ode = f(x,y)
% F - 
%   
ode = [ y(2);
	exp(x)/sqrt(y(1)) ];